Seminars and Colloquia by Series

Thursday, September 29, 2011 - 15:05 , Location: Skiles 006 , David Goldberg , ISyE, Georgia Tech , Organizer:
In this talk, we resolve several questions related to a certain heavy traffic scaling regime (Halfin-Whitt) for parallel server queues, a family of stochastic models which arise in the analysis of service systems.  In particular, we show that the steady-state queue length scales like $O(\sqrt{n})$, and bound the large deviations behavior of the limiting steady-state queue length.  We prove that our bounds are tight for the case of Poisson arrivals.  We also derive the first non-trivial bounds for the steady-state probability that an arriving customer has to wait for service under this scaling.  Our bounds are of a structural nature, hold for all $n$ and all times $t \geq 0$, and have intuitive closed-form representations as the suprema of certain natural processes.  Our upper and lower bounds also exhibit a certain duality relationship, and exemplify a general methodology which may be useful for analyzing a variety of stochastic models.  The first part of the talk is joint work with David Gamarnik.
Thursday, September 22, 2011 - 15:05 , Location: Skiles 006 , Yuri Bakhtin , School of Mathematics, Georgia institute of Technology , Organizer:
The Burgers equation is a nonlinear PDE and one of the basic hydrodynamic models. The ergodic theory of the Burgers turbulence began with the work of E, Khanin, Mazel, Sinai (Ann. Math. 2000). In their paper and in subsequent papers by Khanin and his coauthors, the compact case (Burgers on a circle or torus) was studied. In this talk, I will discuss the noncompact case. The main object is optimal paths through clouds of Poissonian points.
Thursday, September 15, 2011 - 15:05 , Location: Skiles 006 , Shannon L. Starr , University of Rochester , , Organizer:
The Potts antiferromagnet on a random graph is a model problem from disordered systems, statistical mechanics with random Hamiltonians. Bayati, Gamarnik and Tetali showed that the free energy exists in the thermodynamic limit, and demonstrated the applicability of an interpolation method similar to one used by Guerra and Toninelli, and Franz and Leone for spin glasses. With Contucci, Dommers and Giardina, we applied interpolation to find one-sided bounds for the free energy using the physicists' ``replica symmetric ansatz.'' We also showed that for sufficiently high temperatures, this ansatz is correct. I will describe these results and some open questions which may also be susceptible to the interpolation method.
Thursday, September 8, 2011 - 15:05 , Location: Skyles 006 , Christian houdre , School of mathematics, Georgia institute of Technology , Organizer:
Given a random word of size n whose letters are drawn independently from an ordered alphabet of size m, the fluctuations of the shape of the associated random RSK Young tableaux are investigated, when n and m converge together to infinity. If m does not grow too fast and if the draws are uniform, then the limiting shape is the same as the limiting spectrum of the GUE. In the non-uniform case, a control of both highest probabilities will ensure the convergence of the first row of the tableau, i.e. of the length of the longest increasing subsequence of the word, towards the Tracy?Widom distribution.
Thursday, September 1, 2011 - 15:05 , Location: Skiles 006 , Joseph Salmon , Electrical and Computer Engineering, Duke University , , Organizer:
We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing onthe exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads tosharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures such as least square regression,kernel ridge regression, shrinking estimators and many other estimators used in the literatureon statistical inverse problems. As a consequence, we show that the proposed aggregate provides an adaptive estimator in the exact minimax sense without neither discretizing the rangeof tuning parameters nor splitting the set of observations. We also illustrate numerically thegood performance achieved by the exponentially weighted aggregate. (This is a joint work with Arnak Dalalyan.)
Thursday, May 12, 2011 - 15:05 , Location: Skiles 005 , Jean-Christophe Breton , Universite de Rennes , Organizer: Christian Houdre
We consider weighted random ball model driven by a Poisson random measure on \Bbb{R}^d\times \Bbb{R}^+\times \Bbb{R} with product heavy tailed intensity and we are interested in the functional describing the contribution of the model in some configurations of \Bbb{R}^d. The fluctuations of such functionals are investigated under different types of scaling and the talk will discuss the possible limits. Such models arise in communication network to represent the transmission of information emitted by stations distributed according to the Poisson measure.
Thursday, April 21, 2011 - 15:05 , Location: Skiles 005 , Wlodek Bryc , University of Cincinnati , Organizer: Christian Houdre

Hosted by Christian Houdre and Liang Peng.

In this talk I will discuss random matrices that are matricial analogs of the well known binomial, Poisson, and negative binomial random variables. The common thread is the conditional variance of X given S = X+X', which is a quadratic polynomial in S and in the univariate case describes the family of six Meixner laws that will be described in the talk. The Laplace transform of a general n by n Meixner matrix ensemble satisfies a system of PDEs which is explicitly solvable for n = 2. The solutions lead to a family of six non-trivial 2 by 2 Meixner matrix ensembles. Constructions for the "elliptic cases" generalize to n by n matrices. The talk is based on joint work with Gerard Letac.
Thursday, April 14, 2011 - 15:00 , Location: Skiles 171 , Fabio Machado , USP san paulo Brazil , Organizer: Heinrich Matzinger
We study four discrete time stochastic systems on $\bbN$ modelingprocesses of rumour spreading. The involved individuals can eitherhave an active ora passive role, speaking up or asking for the rumour. The appetite inspreading or hearing the rumour is represented by a set of randomvariables whose distributionsmay depend on the individuals. Our goal is to understand - based on those randomvariables distribution - whether the probability of having an infiniteset of individuals knowing the rumour is positive or not.
Thursday, April 7, 2011 - 15:05 , Location: Skiles 005 , Heinrich Matzinger , Georgia Tech , , Organizer: Heinrich Matzinger
We consider two random sequences of equal length n and the alignments with gaps corresponding to their Longest Common Subsequences. These alignments are called optimal alignments. What are the properties of these alignments? What are the proportion of different aligned letter pairs? Are there concentration of measure properties for these proportions? We will see that the convex geometry of the asymptotic limit set of empirical distributions seen along alignments can determine the answer to the above questions.
Thursday, March 31, 2011 - 15:05 , Location: Skiles 005 , Jan Rosinski , University of Tennessee, Knoxville , Organizer:
Semimartingales constitute the larges class of "good integrators" for which Ito integral could reasonably be defined and the stochastic analysis machinery applied. In this talk we identify semimartingales within certain infinitely divisible processes. Examples include stationary (but not independent) increment processes, such as fractional and moving average processes, as well as their mixtures. Such processes are non-Markovian, often possess long range memory, and are of interest as stochastic integrators. The talk is based on a joint work with Andreas Basse-O'Connor.