I am co-organizing a virtual Probability Seminar with Wei-Kuo Chen and Arnab Sen at University of Minnesota for
the Spring 2026 semester. Please email me to get the Zoom link for the seminar series.
The seminar is held on Fridays at 2:30pm (Eastern Time), unless otherwise noted below.
| 01/30/2026 | Sergey Bobkov (U Minnesota) |
| Title: Quantified Cramer-Wold continuity theorem for Kantorovich and Zolotarev distances. | |
| Abstract: Upper bounds for the Kantorovich and Zolotarev distances for
probability measures on multidimensional Euclidean spaces are given in
terms of similar distances between one dimensional projections of the
measures. This quantifies the Cramer-Wold continuity theorem about the
weak convergence of probability measures. Joint work with Friedrich Götze. | |
| 02/06/2026 | Jiaqi Liu (Lehigh) |
| Title: Conformal loop ensemble and its geometric properties. | |
| Abstract The conformal loop ensemble (CLE) is a natural conformally invariant probability measure on infinite collections of non-crossing loops, where each loop looks like an SLE curve. CLE has been proven or conjectured to describe the scaling limit of interfaces of many statistical physics models. Understanding its geometric properties is useful for explaining how it emerges in these scaling limits. In this talk, we focus on the extremal distance, which gives a conformally invariant way of measuring the distance between two loops. We show that the reweighted distribution of extremal distances between CLE loops can be expressed as linear combinations of first exit times and last hitting times of a one-dimensional Brownian motion. This is based on joint work with Nina Holden and Xin Sun. | |
| 02/13/2026 | Arnab Chatterjee (TU Dortmund) |
| Title: Belief Propagation Guided Decimation on random k-XORSAT. | |
| Abstract: We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random k-XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a strictly positive probability Ω(1) that we compute explicitly, but beyond which the algorithm with high probability fails to find a satisfying assignment. In addition, we analyse a thought experiment called the decimation process for which we identify a (non-) reconstruction and a condensation phase transition. The main results of the present work confirm physics predictions from [RTS: J. Stat. Mech. 2009] that link the phase transitions of the decimation process with the performance of the algorithm, and improve over partial results from a recent article [Yung: Proc. ICALP 2024]. | |
| 02/20/2026 | Ruoyu Wu (Iowa State) |
| Title: Some large deviation principles for load-balancing queueing systems. | |
| Abstract: We consider the large-scale load-balancing queueing system under the Join-the-Shortest-Queue-d(n) policy with diverging d(n). The system consists of one dispatcher and n servers. When a task arrives at the dispatcher, d(n) servers are chosen uniformly at random and the task is routed to the one with the shortest queue length. We establish large deviation principles for the system occupancy process, for d(n)=n and for generally diverging d(n). Proofs rely on certain variational representations for exponential functionals of Poisson random measures, stochastic controls, and weak convergence arguments. This is based on joint works with Amarjit Budhiraja and Eric Friedlander. | |
| 02/27/2026 | Ani Sridhar (NJIT) |
| Title: Detecting super-spreaders in network epidemics. | |
| Abstract: Suppose that a continuous-time, stochastic diffusion (i.e., the Susceptible-Infected process) spreads on an unknown graph. We only observe the time at which the diffusion reaches each vertex, i.e., the set of infection times. What can be learned about the unknown graph from the infection times? While there is far too little information to learn individual edges in the graph, we show that certain high-level properties -- such as the number of vertices of sufficiently high degree, or super-spreaders -- can surprisingly be determined with certainty. To achieve this goal, we develop a suite of algorithms that can efficiently detect vertices of degree asymptotically greater than sqrt(n) from infection times, for a natural and general class of graphs with n vertices. To complement these results, we show that our algorithms are information-theoretically optimal: there exist graphs for which it is impossible to tell whether vertices of degree larger than n1/2-ε exist from vertices' infection times, for any ε > 0. Finally, we discuss the broader implications of our ideas for change-point detection in non-stationary point processes. This talk is based on joint work with Anna Brandenberger (MIT) and Elchanan Mossel (MIT). | |
| 03/06/2026 | Lihu Xu (Michigan State) |
| Title: Probability Approximations by Stein’s Method. | |
| Abstract: In this talk, I will review recent developments in probability approximations using Stein’s method, focusing on the following topics: (1) Stable law convergence with explicit rates; (2) Diffusion approximations with explicit rates; (3) Long-term Smoluchowski–Kramers approximation with explicit rates. The main approach in these results is Stein’s method, which relies on the regularity estimates of Stein’s equation and the choice of suitable Markov process. | |
| 03/13/2026 | Spring Break at LU and UMN |
| 03/20/2026 | Robin Khanfir (McGill University) |
| Title: Horton—Strahler number, height, and an intriguing correspondence. | |
| Abstract: The Horton--Strahler number, also known as the register function, is a natural measure of the branching complexity of a rooted tree T. Indeed, it is the height of the largest perfect binary tree that can be homeomorphically embedded into T. Quite surprisingly, the number of full binary trees with n internal vertices and Horton--Strahler number s is known to be the same as the number of Dyck paths of length 2n whose height h is such that s equals the integer part of log2(1+h). In this talk, we will shed new light on this combinatorial identity, fortuitously discovered 50 years ago, while proposing a more precise version of it. This study will take us from discrete combinatorics to continuum random geometry. Indeed, (a metric analog of) the Horton--Strahler number of the Brownian tree has the same law as the maximum of the Brownian excursion. | |
| 03/27/2026 | Devraj Duggal (UMN) |
| Title: Rearrangements and infimum convolutions. | |
| Abstract: A general comparison result for inf-convolution operators related to rearrangements is provided. As a consequence, comparison results are derived for the Laplace and Polar transforms and a class of parabolic partial differential equations. Lastly, we revisit pre-existing proofs of a functional form of the Blaschke-Santalo inequality due to Keith Ball. This work is joint with James Melbourne and Cyril Roberto. | |
| 04/03/2026 | Theo McKenzie (Stanford) |
| Title: Gaussian behavior of eigenvectors in sparse random graphs. | |
| Abstract: Sparse random graphs are widely viewed as discrete models of chaotic physical systems. Heuristically, this suggests that eigenvectors of the adjacency operator should exhibit Gaussian statistics. We prove that a broad class of random graphs, including both random regular graphs and irregular configuration-type models, display local Gaussian behavior. Notably, our approach does not rely on local law universality; instead, it is based on combinatorial and entropy-based arguments intrinsic to the graph structure. | |
| 04/17/2026 | Felix Leditzky (UIUC) |
| Title: TBA | |
| Abstract: TBA | |
| 04/24/2026 | Johannes Bäumler (UCLA) |
| Title: TBA | |
| Abstract: TBA | |