Seminars and Colloquia by Series

Some upper and lower bounds on the variance of functions of independent random variables

Series
Probability Working Seminar
Time
Tuesday, February 3, 2026 - 15:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Christian Houdré – Georgia Tech –

Please Note: Third of several talks.

I'll present various methods, some old, some new,  leading to estimates on the variance of $f(X_1, X_2, \dots, X_n)$ where  

$X_1, X_2, \dots, X_n$ are independent random variables.  These methods will be illustrated with various examples.

Some upper and lower bounds on the variance of functions of independent random variables

Series
Probability Working Seminar
Time
Tuesday, January 20, 2026 - 15:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Christian Houdré – Georgia Tech –

Please Note: Second of several talks.

I'll present various methods, some old, some new,  leading to estimates on the variance of $f(X_1, X_2, \dots, X_n)$ where  

$X_1, X_2, \dots, X_n$ are independent random variables.  These methods will be illustrated with various examples.

Some upper and lower bounds on the variance of functions of independent random variables

Series
Probability Working Seminar
Time
Tuesday, January 13, 2026 - 15:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Christian Houdré – Georgia Institute of Technology –

Please Note: First of several talks.

I'll present various methods, some old, some new,  leading to estimates on the variance of $f(X_1, X_2, \dots, X_n)$ where  

$X_1, X_2, \dots, X_n$ are independent random variables.  These methods will be illustrated with various examples.

Self-avoiding walks and sampling in statistical physics models

Series
Probability Working Seminar
Time
Friday, October 15, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 249
Speaker
Ricardo Restrepo – School of Math, Georgia Tech
 We will discuss the role that self-avoiding walks play in sampling 'physical' models on graphs, allowing to translate  the complicated calculation of the marginals to a tree recurrence which, under the appropriate conditions (e.g. some form of 'spatial mixing'), reduces to a polynomial recurrence. This talk is mainly based on Dror Weitz' article "Counting independent sets up to the tree threshold". 

Concentration inequalities for matrix martingales

Series
Probability Working Seminar
Time
Friday, October 8, 2010 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 249
Speaker
Stas Minsker – School of Math, Georgia Tech
We will present probability inequalities for the sums of independent, selfadjoint random matrices. The focus is made on noncommutative generalizations of the classical bounds of Azuma, Bernstein, Cherno ff, Hoeffding, among others. These inequalities imply concentration results for the empirical covariance matrices. No preliminary knowledge of probability theory will be assumed. (The talk is based on a paper by J. Tropp).

The effects of small noise random perturbation for some problems without unique solutions.

Series
Probability Working Seminar
Time
Friday, October 1, 2010 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 249
Speaker
Sergio Almada – School of Math, Georgia Tech
We consider the small noise perturbation (in the Ito sense) of a one dimensional ODE. We study the case in which the ODE has not unique solution, but the SDE does. A particular setting of this sort is studied and the properties of the solution are obtained when the noise level vanishes. We relate this to give an example of a 1-dimensional transport equation without uniqueness of weak solution. We show how by a suitable random noise perturbation, the stochastic equation is well posed and study what the limit is when the noise level tends to zero.

From concentration to isoperimetry by semigroup proofs

Series
Probability Working Seminar
Time
Friday, April 2, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Linwei Xin – Georgia Tech
 It is well known that isoperimetric type inequalities can imply concentration inequalities, but the reverse is not true generally. However, recently E Milman and M Ledoux proved that under some convex assumption of the Ricci curvature, the reverse is true in the Riemannian manifold setting. In this talk, we will focus on the semigroup tools in their papers. First, we introduce some classic methods to obtain concentration inequalities, i.e. from isoperimetric inequalities, Poincare's inequalities, log-Sobolev inequalities, and transportation inequalities. Second, by using semigroup tools, we will prove some kind of concentration inequalities, which then implies linear isoperimetry and super isoperimetry. 

TIME CHANGE !!!! TIME CHANGE!!! A Stochastic Lagrangian approach to the Navier-Stokes equations

Series
Probability Working Seminar
Time
Friday, March 19, 2010 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 169
Speaker
Sergio Almada – Georgia Tech
In this talk I will present an elementary short proof of the existence of global in time H¨older continuous solutions for the Stochastic Navier-Stokes equation with small initial data ( in both, 3 and 2 dimensions). The proof is based on a Stochastic Lagrangian formulation of the Navier-Strokes equations. This talk summarizes several papers by Iyer, Mattingly and Constantin.

Harris' ergodic theorem for Markov chains revisited

Series
Probability Working Seminar
Time
Friday, February 19, 2010 - 15:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 169
Speaker
Tobias Hurth – Georgia Tech
In my talk, I will present the main results of a recent article by Martin Hairer and Jonathan Mattingly on an ergodic theorem for Markov chains. I will consider Markov chains evolving in discrete time on an abstract, possibly uncountable, state space. Under certain regularity assumptions on the chain's transition kernel, such as the existence of a Foster-Lyapunov function with small level sets (what exactly is meant by that will be thoroughly explained in the talk), one can establish the existence and uniqueness of a stationary distribution. I will focus on a new proof technique for that theorem which relies on a family of metrics on the set of probability measures living on the state space. The main result of my talk will be a strict contraction estimate involving these metrics.

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