I did my Phd (I defended it 29/06/2017), at the university Paul Sabatier (Toulouse), under the supervision of Michel Ledoux. After one year at the university of Angers (LAREMA) (with an ATER position), I am now teacher in high school (Beaupré at Haubourdin).
Basically : the goal is to bound from above the variance of the maximum of Gaussian family when Poincaré’s inequality (satisfied by Gaussian measures) provides sub optimal bound. For example : consider X_i, for i=1 to n, a sequence of i.i.d. standard Gaussian random variables. Poincaré’s inequality implies that the variance of the maximum of the X_i’s is bounded by 1. In fact, one can show that the variance is of order 1/log(n).
This simple example is a prototype of the so-called superconcentration phenomenon introduced by S.Chatterjee in his book Superconcentration and related topics. Such phenomenon appears naturally in a lot of differents mathematical areas : percolation, spin glasses, Gaussian free field, random matrix ….
The subject of my thesis was to find new examples of superconcentration, new methods to obtain the sharpest bound for the variance of the maximum of Gaussian family and concentration inequalities reflecting such variance’s bounds.
I am also interested in functional inequalities, concentration of measure phenomenon, boolean analysis, optimal transport and spin glasses theory.
e-mail : kevin.tanguyATuniv-angersDOTfr
LAREMA, Faculté des Sciences
2 Boulevard Lavoisier
49045 Angers cedex 01