I did my Phd (I defended it 29/06/2017), at the university Paul Sabatier (Toulouse), under the supervision of  Michel Ledoux. I am studying  superconcentration phenomenon (the terminology came from an article of S.Chatterjee : Disorder, chaos and multiple valleys).

Basically : the goal is to bound from above the variance of the maximum of Gaussian familly Gaussiennes when the Poincaré 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 inequality implues 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 area  : percolation, spin glasses, Gaussian free field, random matrix ….

The subject of my thesis is to find new examples of superconcentration, new methods to obtain the sharpest bound for the variance of the maximum of Gaussian family and concentration inequality reflecting the variance bounds.

e-mail : ktanguyATmathDOTuniv-toulouseDOTfr



Office : 207 bâtiment 1R1 2ème étage
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Institut Mathématique de Toulouse
Université Paul Sabatier
118, Route de Narbonne

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