Publications
Preprints:
Nhat-Thang Le and Laurent Miclo. Swarm dynamics for global optimisation on finite sets. April 2024.
Laurent Miclo. On finite interweaving relations. March 2024.
Simon Apers and Laurent Miclo. Quantum walks, the discrete wave equation and Chebyshev polynomials. February 2024.
Persi Diaconis and Laurent Miclo. On a Markov construction of couplings. May 2023.
Laurent Miclo. On the convergence of global-optimization fraudulent stochastic algorithms. April 2023.
Accepted papers:
Laurent Miclo. On the Helmholtz decomposition for finite Markov processes. To appear in Séminaire de Probabilités, Springer. Lect. Notes Math., 2024.
Articles:
[97] Marc Arnaudon, Koléhè Coulibaly-Pasquier and Laurent Miclo. The stochastic renormalized mean curvature flow for planar convex sets. To appear in
Electronic Journal of Probability, 24, paper 183, 1-43, 2024.
[96] Laurent Miclo. On the complex eigenvalues of finite Markov generators. To appear in Electronic Communications in Probability,
29, paper 76, 1-12, 2024.
[95] Aris Daniilidis, Laurent Miclo and David Salas. Descent modulus and applications. Journal of Functional Analysis, 287(11): 54 p., 2024.
[94] Marc Arnaudon, Koléhè Coulibaly-Pasquier and Laurent Miclo. On Markov intertwining relations and primal conditioning. J. Theoret. Probab., 37(3), 2425-2456, 2024.
[93] Jérôme Bolte, Laurent Miclo and Stéphane Villeneuve. Swarm gradient dynamics for global optimization: the density case. Mathematical Programming, 205(1-2,A): 661-701, 2024.
[92] Marc Arnaudon, Koléhè Coulibaly-Pasquier and Laurent Miclo. On the separation cut-off phenomenon for Brownian motions on high dimensional spheres. Bernoulli, 30(2): 1007-1028, 2024.
[91] Marc Arnaudon, Koléhè Coulibaly-Pasquier and Laurent Miclo. Construction of set-valued dual processes on manifolds. Journal de l’École polytechnique — Mathématiques, 11: 473-522, 2024.
[90] Laurent Miclo. Strong stationary times for finite Heisenberg walks. ESAIM: Probability and Statistics, 27: 515-557, 2023.
[89] Sourav Chatterjee, Persi Diaconis and Laurent Miclo. A random walk on the Rado graph. In Toeplitz Operators and Random Matrices, In Memory of Harold Widom, Birkhäuser/Springer Nature, 2022.
[88] Laurent Miclo. On metastability. Probability Theory and Related Fields, no 1-2: 275-322, 2022.
[87] Laurent Miclo and Pierre Patie. On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes. Séminaire de Probabilités, Springer. Lect. Notes Math. 2301, 117-141, 2022.
[86] Laurent Miclo, Pierre Patie and Rohan Sarkar. Discrete self-similar and ergodic Markov chains. Annals of Probability, 50(6): 2085-2132, 2022.
[85] Laurent Miclo, Daniel Spiro and Jörgen Weibull. Optimal epidemic suppression under an ICU constraint. Journal of Mathematical Economics, no 101: 17pp., 2022.
[84] Koléhè Coulibaly-Pasquier and Laurent Miclo. On the evolution by duality of domains on manifolds. Les Mémoires de la SMF, no 172: 110 pp., 2021.
[83] Laurent Miclo and Stéphane Villeneuve. On the forward algorithm for stopping problems on continuous-time Markov chains. Journal of Applied Probability, 58(4): 1043-1063, 2021.
[82] Laurent Miclo and Chi Zhang. On a family of isospectral pure-birth processes. ALEA Lat. Am. J. Probab. Math. Stat., 18(2): 1759-1771, 2021.
[81] Eyal Castiel, Sem Borst, Laurent Miclo, Florian Simatos and Phil Whiting. Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms. Annals of Applied Probability, 31(2): 941-971, 2021.
[80] Laurent Miclo and Pierre Patie. On interweaving relations. Journal of Functional Analysis, 280(3):54 pp., 2021.
[79] Laurent Miclo. On the construction of set-valued dual processes. Electronic Journal of Probability, 25(paper 6):1-64, 2020.
[78] Asma Hassannezhad and Laurent Miclo. Higher order Cheeger inequalities for Steklov eigenvalues. Annales Scientifiques de l’École Normale Supérieure, 53(1):43-88, 2020.
[77] Vivek Borkar and Laurent Miclo. On the fastest finite Markov processes. Journal of Mathematical Analysis and Applications 481(2):43pp., 2020.
[76] Laurent Miclo. Isoperimetric stability of boundary barycenters in the plane. Annales Mathématiques Blaise Pascal, 26(1):67–80, 2019.
[75] Laurent Miclo. Complex intertwinings and quantification of discrete free motions. ESAIM: Probability and Statistics 23:409-429, 2019.
[74] Laurent Miclo and Pierre Patie. On a gateway between continuous and discrete Bessel and Laguerre processes. Annales Henri Lebesgue 2:59-98, 2019.
[73] Laurent Miclo. On the Markov commutator. Bulletin des Sciences Mathématiques 154:1–35, 2019.
[72] Laurent Miclo. Some drawbacks of finite modified logarithmic Sobolev inequalities. Mathematica Scandinavica 123(1):147-159, 2018.
[71] Laurent Miclo. On the Markovian similarity. Séminaire de Probabilités XLIX :375-403, 2018.
[70] Emmanuel Boissard, Patrick Cattiaux, Arnaud Guillin and Laurent Miclo. Ornstein-Uhlenbeck Pinball and the Poincaré Inequality in a Punctured Domain. Séminaire de Probabilités XLIX :1-55, 2018.
[69] Laurent Miclo, Duality and hypoellipticity: one-dimensional case studies. Electronic Journal of Probability, 22(paper 91) :1-38, 2017.
[68] Shui Feng, Laurent Miclo and Feng-Yu Wang, Poincaré inequality for Dirichlet distributions and infinite-dimensional generalizations. ALEA Lat. Am. J. Probab. Math. Stat., 14(1) :361-380, 2017.
[67] Daniel Bump, Persi Diaconis, Angela Hicks, Laurent Miclo and Harold Widom. Useful bounds on the extreme eigenvalues and vectors of matrices for Harper’s operators. Large truncated Toeplitz matrices, Toeplitz operators, and related topics :235–265, Operator Theory: Advances and Applications, 259, Birkhäuser/Springer, Cham, 2017.
[66] Laurent Miclo. On the hypergroup property. Annales de la Faculté des Sciences de Toulouse, Mathématiques, 26(6) no. 2 :417–435, 2017.
[65] Daniel Bump, Persi Diaconis, Angela Hicks, Laurent Miclo and Harold Widom. An exercise(?) in Fourier analysis on the Heisenberg group. Annales de la Faculté des Sciences de Toulouse, Mathématiques, 26(6) no. 2 :263–288, 2017.
[64] Laurent Miclo. Strong stationary times for one-dimensional diffusions. Annales de l’Institut Henri Poincaré Probab. Statist., 53(2) :957–996, 2017.
[63] Marc Arnaudon and Laurent Miclo. A stochastic algorithm finding p-means on the circle. Bernoulli, 22(4):2237–2300, 2016.
[62] Persi Diaconis and Laurent Miclo. Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks. Sci. China Math., 59(2) :205–226, 2016.
[61] Laurent Miclo. On ergodic diffusions on continuous graphs whose centered resolvent admits a trace. J. Math. Anal. Appl., 437(2) :737–753, 2016.
[60] Persi Diaconis and Laurent Miclo. On quantitative convergence to quasi-stationarity. Annales de la Faculté des Sciences de Toulouse, Mathématiques, (6)24(4) :973–1016, 2015.
[59] Laurent Miclo. An absorbing eigentime identity. Markov Processes And Related Fields, 21(2) :249–262, 2015.
[58] Sébastien Gadat, Laurent Miclo and Fabien Panloup. A stochastic model for speculative dynamics. ALEA Lat. Am. J. Probab. Math. Stat., 12 :491–532, 2015.
[57] Laurent Miclo. On hyperboundedness and spectrum of Markov operators. Invent. Math., 200(1) :311–343, 2015.
[56] Marc Arnaudon and Laurent Miclo. A stochastic algorithm finding generalized means on compact manifolds. Stochastic Processes and their Applications, 124 :3463-3479, 2014.
[55] Marc Arnaudon and Laurent Miclo. Means in complete manifolds: uniqueness and approximation. ESAIM: Probability and Statistics, 18 :185-206, 2014.
[54] Laurent Miclo and Pierre Monmarché. Étude spectrale minutieuse de processus moins indécis que les autres. [Detailed spectral study of processes that are less undecided than others]. Lecture Notes in Mathematics 2078, Springer, Berlin. Séminaire de Probabilités XLV :459-481, 2013.
[53] Persi Diaconis and Laurent Miclo. On the spectral analysis of second-order Markov chains. Annales de la Faculté des Sciences de Toulouse, Mathématiques, (6) 22(3) :573–621, 2013.
[52] Sébastien Gadat and Laurent Miclo. Spectral decompositions and L2-operator norms of toy hypocoercive semi-groups.
Kinetic and Related Models, 6(2) :317–372, 2013.
[51] Nicolas Champagnat, Persi Diaconis and Laurent Miclo. On Dirichlet eigenvectors for neutral two-dimensional Markov chains. Electron. J. Probab., 17(63) :1-41, 2012.
[50] Amir Daneshgar, Ramin Javadi and Laurent Miclo. On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes. Stochastic Processes and their Applications, 122(4) :1748–1776, 2012.
[49] André Galligo and Laurent Miclo On the cut-off phenomenon for the transitivity of randomly generated subgroups. Random Structures Algorithms, 40(2) :182–219, 2012.
[48] Persi Diaconis and Laurent Miclo. On barycentric subdivision. Combin. Probab. Comput., 20(2) :213–237, 2011.
[47] Laurent Miclo On absorption times and Dirichlet eigenvalues. ESAIM: Probability and Statistics, 14 :117–150, 2010.
[46] Pierre Del Moral, Laurent Miclo, Frédéric Patras and Sylvain Rubenthaler. The convergence to equilibrium of neutral genetic models. Stochastic Analysis and Applications, 28(1) :123–143, 2010.
[45] Laurent Miclo. Monotonicity of the extremal functions for one-dimensional inequalities of logarithmic Sobolev type. Lecture Notes in Mathematics 1979, Springer, Berlin. Séminaire de Probabilités XLII :103–130, 2009.
[44] Persi Diaconis and Laurent Miclo. On times to quasi-stationarity for birth and death processes. J. Theoret. Probab., 22(3) :558–586, 2009.
[43] Persi Diaconis and Laurent Miclo. On characterizations of Metropolis type algorithms in continuous time. ALEA Lat. Am. J. Probab. Math. Stat., 6 :199–238, 2009.
[42] Laurent Miclo Une condition asymptotique pour le calcul de constantes de Sobolev logarithmiques sur la droite. [An asymptotic condition for computing the logarithmic Sobolev constant on the line]. Annales de l’Institut Henri Poincaré Probab. Statist., 45(1) :146–156, 2009.
[41] Laurent Miclo. Quand est-ce que des bornes de Hardy permettent de calculer une constante de Poincaré exacte sur la droite ?. [When can Hardy bounds be used to calculate an exact Poincaré constant on the line?]. Annales de la Faculté des Sciences de Toulouse, Mathématiques, (6) 17(1) :121–192, 2008.
[40] Laurent Miclo. On eigenfunctions of Markov processes on trees. Probability Theory and Related Fields, 142(3-4) :561–594, 2008.
[39] Ivan Gentil, Arnaud Guillin and Laurent Miclo. Modified logarithmic Sobolev inequalities in null curvature. Revista Matemática Iberoamericana, 23(1) :235–258, 2007.
[38] Pierre Del Moral and Laurent Miclo. Strong propagations of chaos in Moran’s type particle interpretations of Feynman-Kac measures. Stochastic Analysis and Applications, 25(3) :519–575, 2007.
[37] Pierre Del Moral and Laurent Miclo. Self-interacting Markov chains. Stochastic Analysis and Applications, 24(3) :615–660, 2006.
[36] Pierre Del Moral and Laurent Miclo. Dynamiques recuites de type Feynman-Kac: résultats précis et conjectures. [Annealed Feynman-Kac dynamics: precise results and conjectures]. ESAIM: Probability and Statistics, 10 :76–140, 2006.
[35] Ivan Gentil, Arnaud Guillin and Laurent Miclo. Modified logarithmic Sobolev inequalities and transportation inequalities. Probability Theory and Related Fields, 133(3) :409–436, 2005.
[34] Pierre Del Moral and Laurent Miclo. On convergence of chains with occupational self-interactions. Stochastic analysis with applications to mathematical finance. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 460(2041) :325–346, 2004.
[33] Laurent Miclo. Notes on the speed of entropic convergence in the central limit theorem. Stochastic inequalities and applications, Birkhäuser, Basel. Progress in Probability, 56 :129–156, 2003.
[32] Pierre Del Moral, Michel Ledoux and Laurent Miclo. On contraction properties of Markov kernels. Probability Theory and Related Fields, 126(3) :395–420, 2003.
[31] Laurent Miclo. Sur l’inégalité de Sobolev logarithmique des opérateurs de Laguerre à petit paramètre. [Logarithmic Sobolev inequality of small-parameter Laguerre operators]. Lecture Notes in Mathematics 1801, Springer, Berlin. Séminaire de Probabilités XXXVI :222–229, 2003.
[30] Laurent Miclo. About projections of logarithmic Sobolev inequalities. Lecture Notes in Mathematics 1801, Springer, Berlin. Séminaire de Probabilités XXXVI :201–221, 2003.
[29] Pierre Del Moral and Laurent Miclo. Annealed Feynman-Kac models. Communications in Mathematical Physics, 235(2) :191–214, 2003.
[28] Pierre Del Moral and Laurent Miclo. Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman-Kac semigroups. ESAIM: Probability and Statistics, 7 :171–208, 2003.
[27] Pierre Del Moral and Laurent Miclo. On the stability of nonlinear Feynman-Kac semigroups. Annales de la Faculté des Sciences de Toulouse, Mathématiques, (6)11(2) :135–175, 2002.
[26] Laurent Miclo. About relaxation time of finite generalized Metropolis algorithms.
Annals of Applied Probability, 12(4) :1492–1515, 2002.
[25] Pierre Del Moral and Laurent Miclo. Asymptotic results for genetic algorithms with applications to nonlinear estimation. Theoretical aspects of evolutionary computing (Antwerp, 1999), Springer, Berlin. Natural Computing Series, :439–493, 2001.
[24] Pierre Del Moral and Laurent Miclo. Genealogies and increasing propagation of chaos for Feynman-Kac and genetic models.
Annals of Applied Probability, 11(4) :1166–1198, 2001.
[23] Pierre Del Moral, Michael A. Kouritzin and Laurent Miclo. On a class of discrete generation interacting particle systems. Electron. J. Probab., 6(16) :1-26, 2001.
[22] Laurent Miclo and Cyril Roberto. Trous spectraux pour certains algorithmes de Metropolis sur R. [Spectral gaps for certain Metropolis algorithms on R]. Lecture Notes in Mathematics 1729, Springer, Berlin. Séminaire de Probabilités XXXIV :336–352, 2000.
[21] Pierre Del Moral and Laurent Miclo. Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering. Lecture Notes in Mathematics 1729, Springer, Berlin. Séminaire de Probabilités XXXIV :1–145, 2000.
[20] Pierre Del Moral and Laurent Miclo. A Moran particle system approximation of Feynman-Kac formulae. Stochastic Processes and their Applications, 86(2) :193–216, 2000.
[19] Laurent Miclo. An example of application of discrete Hardy’s inequalities. Markov Processes And Related Fields, 5(3) :319–330, 1999.
[18] Laurent Miclo. Relations entre isopérimétrie et trou spectral pour les chaînes de Markov finies. [Relations between isoperimetry and spectral gap for finite Markov chains]. Probability Theory and Related Fields, 114(4) :431–485, 1999.
[17] Pierre Del Moral and Laurent Miclo. On the convergence and applications of generalized simulated annealing. SIAM Journal on Control and Optimization, 37(4) :1222–1250, 1999.
[16] Laurent Miclo. Une majoration sous-exponentielle pour la convergence de l’entropie des chaînes de Markov à trou spectral. [Subexponential upper bound for the convergence of the entropy of Markov chains with spectral gap]. Annales de l’Institut Henri Poincaré Probab. Statist., 35(3) :261–311, 1999.
[15] Laurent Miclo. Trous spectraux à basse température: un contre-exemple à un comportement asymptotique escompté. [Low-temperature spectral gaps: a counterexample to a discounted asymptotic behavior]. Lecture Notes in Mathematics 1686, Springer, Berlin. Séminaire de Probabilités XXXII :36–55, 1998.
[14] Laurent Miclo. Sur les temps d’occupations des processus de Markov finis inhomogènes à basse température. [Occupation times of low-temperature nonhomogeneous finite Markov processes]. Stochastics Stochastics Rep. 63(1-2) :65–137, 1998.
[13] Laurent Miclo. Une variante de l’inégalité de Cheeger pour les chaînes de Markov finies. [A variant of the Cheeger inequality for finite Markov chains]. ESAIM: Probability and Statistics, 2 :1–21, 1998.
[12] Laurent Miclo. Remarques sur l’hypercontractivité et l’évolution de l’entropie pour des chaînes de Markov finies. [Remarks on hypercontractivity and evolution of entropy in finite Markov chains]. Lecture Notes in Mathematics 1655, Springer, Berlin. Séminaire de Probabilités XXXI :136–167, 1997.
[11] Laurent Miclo. Recuit simulé partiel. [Partial simulated annealing]. Stochastic Processes and their Applications, 65(2) :281–298, 1996.
[10] Laurent Miclo. Sur les problèmes de sortie discrets inhomogènes. [On inhomogeneous discrete exit problems].
Annals of Applied Probability, 6(4) :1112–1156, 1996.
[9] Laurent Miclo. Une étude des algorithmes de recuit simulé sous-admissibles. [A study of subadmissible simulated annealing algorithms]. Annales de la Faculté des Sciences de Toulouse, Mathématiques, (6)4(4) :819–877, 1995.
[8] Laurent Miclo. Comportement de spectres d’opérateurs de Schrödinger à basse température. [Low-temperature behavior of spectra of Schrödinger operators]. Bulletin des Sciences Mathématiques, 119(6) :529–553, 1995.
[7] Laurent Miclo. Remarques sur l’ergodicité des algorithmes de recuit simulé sur un graphe. [Remarks on the ergodicity of simulated annealing algorithms on graphs]. Stochastic Processes and their Applications, 58(2) :329–360, 1995.
[6] Laurent Miclo. Un algorithme de recuit simulé couplé avec une diffusion. [A simulated annealing algorithm coupled with a diffusion]. Stochastics Stochastics Rep., 46(3-4) :193–268, 1994.
[5] Laurent Miclo. Recuit simulé sans potentiel sur une variété riemannienne compacte. [Simulated annealing without potential on a compact Riemannian manifold]. Stochastics Stochastics Rep., 41(1-2) :23–56, 1992.
[4] Laurent Miclo. Recuit simulé sans potentiel sur un ensemble fini. [Simulated annealing without potential on a finite set]. Lecture Notes in Mathematics 1526, Springer, Berlin. Séminaire de Probabilités XXVI :47–60, 1992.
[3] Laurent Miclo. Recuit simulé sur \(\mathbb{R}^n\). Étude de l’évolution de l’énergie libre. [Simulated annealing in \(\mathbb{R}^n\). Study of the evolution of free energy]. Annales de l’Institut Henri Poincaré Probab. Statist., 28(2) :235–266, 1992.
[2] Laurent Miclo. Comportement asymptotique de l’énergie libre spécifique. Application à l’ergodicité et au recuit simulé en dimension infinie. [Asymptotic behavior of specific free energy. Application to ergodicity and simulated annealing in infinite dimension]. Annales de l’Institut Henri Poincaré Probab. Statist., 28(2) :195–234, 1992.
[1] Laurent Miclo. Recuit simulé sur \(\mathbb{R}^n\). [Simulated annealing on \(\mathbb{R}^n\)]. C. R. Acad. Sci. Paris Sér. I Math., 310(11) :783–786, 1990.
Unpublished manuscripts:
Claire Delplancke and Laurent Miclo. Berry-Esseen bounds for the χ2-distance in the Central Limit Theorem: a Markovian approach. 2017.
Laurent Miclo. A singular large deviation phenomenon for some exit times. 2000.
Laurent Miclo. Problème de sortie discret et théorèmes limites pour les temps d’occupations du recuit simulé. [Simulated annealing: discrete exit problem and limit theorems for occupation times]. 1995.
Laurent Miclo. Recuit simulé relativement à une famille de potentiels d’interactions de rang fini et invariante par translations. [Simulated annealing with respect to finite range and translation invariant interaction potential families]. 1991.