Georgia Institute of Technology College of Sciences

TBA

A basic question in random matrix theory is how likely a matrix is to have a large rank. For many classical models, this probability decays extremely quickly, but the strongest results often rely on the entries being identically distributed. In this talk, I will discuss how to obtain the same exponential scale for matrices with fully independent, non-identically distributed entries under only a uniform anti-concentration assumption and explain the main ideas that make this possible.

Abstract: In the early 2000s, substantial work was devoted to understanding the generally distributed processor-sharing queue, which can be viewed as an idealization of round-robin or time-sharing protocols arising in computer-system applications. The fluid limit for a processor-sharing queue with reneging was established, but the diffusion limit for a processor-sharing queue with impatience was obtained only under a “soft deadlines” formulation, in which the patience times of jobs are tracked but jobs do not actually leave the queue when their patience times expire. This limitation was largely a consequence of the methodology underlying that research program: much of the analysis relied on heavy-traffic limits and the state-space-collapse framework introduced by Bramson and Williams, which is not naturally suited to systems with reneging. More recent work has developed methods for obtaining diffusion approximations of measure-valued queueing systems using classical central limit theorem analysis, martingale methods, and SPDE-valued limits (see work by Ramanan and by the author of this talk). Using these methods, the diffusion approximation for a processor-sharing queue with true reneging can be obtained.

Bio: Eva Loeser is a postdoctoral research associate in the Applied Probability Group in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill. Her research interests include stochastic processes, particularly fluid and diffusion approximations of stochastic systems, high-dimensional stochastic processes, and universal limiting objects such as stochastic partial differential equations (SPDEs) and semimartingale reflecting Brownian motions (SRBMs). The models she studies arise in applications including systems biology, computer systems, queueing theory, operations research, and mathematical physics.

We study robust D-optimal experiment design in generalized linear models, choosing design weights to maximize the worst-case determinant of the Fisher information matrix over a convex parameter uncertainty set. This can be thought of as the natural generalization of D-optimal design in linear regression, and the key challenge is that the information matrix depends on the parameter, so the resulting minimax problem is generally not convex-concave. We show that the desired convexity-concavity, in fact, reduces to a scalar curvature condition on the log-partition function of the exponential family, namely its second derivative h must satisfy the inequality h''h ≥ q(h')² for some q > 1. This insight is connected to the notion of Volumetric Barrier (VB) convexity for self-concordant functions, a result first introduced by Tseng et al (2025) in the context of online quantum state estimation. With self-concordant barriers on the design weights simplex and the parameter uncertainty set, the regularized saddle objective becomes a self-concordant convex-concave (SCCC) function, enabling efficient minimax interior-point methods developed by Nemirovski. We also consider the generalization of the framework, where convexity in the model parameter breaks, but the q-inequality holds up to a deficit proportional to h; in this case, our methods are just as applicable. It turns out that this class includes all canonical GLMs, and we identify logistic regression as the hardest model in the class.

This joint work with Dmitrii Ostrovskii.