Date/Time : 14 Oct 2026 15:15
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Stefan Junk, Gakushuin University

We consider the directed polymer model in dimensions d≥3, which describes random paths affected by an i.i.d. space-time random environment. In the weak disorder (high temperature) phase, the associated martingale at inverse temperature β is Lp-bounded for 1 ≤ p < p*, where p* = p*(β) > 1 is the critical moment exponent. We show that p*(β) is a (locally) Lipschitz-continuous function of β in the interior of the weak disorder phase. Joint work with Hubert Lacoin (IMPA).

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Date/Time : 09 Sep 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Sam McKeown, Nanyang Technological University

Last passage percolation (LPP) is a particularly simple and well-studied model of random geometry on a lattice. While questions on the typical shape of the geodesic between two points have attracted much attention in recent decades, we instead consider the shape of the “most typical” geodesic. A counterintuitive folk conjecture states that these modal geodesics should be the most extreme admissible paths. We give some quantitative results in this direction. In the integrable case of exponential LPP, we show that extreme paths are close to modal in a precise sense. Based on joint work with Shuta Nakajima.

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Date/Time : 13 Aug 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Boaz Klartag, Tel Aviv University and Weizmann Institute of Science

We survey progress from the past five years on the distribution of mass in high-dimensional convex bodies and in probability distributions with convexity properties. The concentration of measure phenomenon has traditionally been studied in highly regular or structured settings, such as spheres, Hamming cubes, Gaussian measures, Markov chains, and martingales. It turns out that convexity assumptions provide an alternative source of regularity in high dimensions with remarkably similar features: Lipschitz functions are highly concentrated, the isoperimetric problem is nearly saturated by half-spaces (up to logarithmic factors), and the central limit theorem is nearly as strong as in the setting of independent random variables. The main developments discussed include the resolution of Bourgain’s slicing problem and the Variance Conjecture, as well as recent progress on the isoperimetric problem for high-dimensional convex bodies. Based on joint work with P. Bizeul and J. Lehec.

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Date/Time : 15 Jul 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Luca Makowiec, Leipzig University

In this talk, we consider a special instance of a random spanning tree in random environment on the complete graph. Each edge is given weight infinity with probability 1/|V| and weight one otherwise. We will discuss a result about the approximate order of the diameter of this tree. In particular, we will explain how a critical Erdős–Rényi graph formed by the infinite-weight edges influences the geometry of the spanning tree. Along the way, we will encounter interesting results and proof techniques associated with the birthday problem and their relation to (weighted) uniform spanning trees (USTs).

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Date/Time : 30 Jun 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lingfu Zhang, California Institute of Technology

A central object in the strong KPZ universality class is the directed landscape. It is a random planar metric and the universal 1:2:3 scaling limit of planar random metrics generated by i.i.d. noise. In this talk, I will discuss joint work with Duncan Dauvergne, where we construct the directed landscape in the half-space. The presence of a boundary gives rise to rich new behavior. We also prove convergence to this object for two discrete models: half-space exponential last-passage percolation and half-space colored TASEP. No prior background in this topic will be assumed.

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Date/Time : 07 May 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Colin Piernot, EPFL

I will talk about the work (joint with Kexing Ying, EPFL) https://arxiv.org/abs/2604.08623, where we study the large-scale behavior of solutions to the Allen-Cahn reaction-diffusion equation with short range Gaussian initial data in dimension more than 3. Under diffusive rescaling, the non-linearity formally vanishes on large scales in this case. Accordingly, we prove a central limit theorem for the rescaled solution, more precisely, that it converges to the solution of the heat equation started from a white noise. The initial conditions for the limit depend non-trivially both on the source of randomness and on the non-linearity.

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Date/Time : 29 Apr 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Cesar Cuenca, Ohio State University

Following a discussion of the continuous Gaussian beta ensemble and the classical Law of Large Numbers (LLN) for its empirical measures in the regimes of fixed and high temperature, we switch to the setting of discrete-space particle systems. By using Fourier transforms based on Jack symmetric polynomials, we study discrete N-particle ensembles in the regime where the inverse temperature parameter tends to zero, simultaneously as the number of particles in the system tends to infinity. We prove the LLN and characterize the limiting measure in terms of a moment problem. For fixed-time distributions of the discrete beta-Dyson Brownian motion, we calculate the densities of the limiting measures and express them in terms of the zeroes of certain entire functions and in terms of the eigenvalues of Jacobi operators. This talk is based on joint works with Florent Benaych-Georges, Vadim Gorin and Maciej Dolega.

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Date/Time : 04 Feb 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Gunter Schuetz, University of Lisbon

The symmetric Dyson exclusion process (SDEP) is a stochastic interacting particle system with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric simple exclusion process and as a discrete version of Dyson’s Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. This allows for proving an explicit formula for the time evolution of the expected microscopic particle density. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling and non-local hydrodynamics where the current is a genuinely non-local functional of the density given by a Hilbert transform. This non-local one-field description is equivalent to a local complex Burgers equation for finite particle density. Closed evolution formulas allow us to solve the melting of single and double block initial states, producing limit shapes and arctic curves that agree with large-scale Monte Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions.

(joint work with J. Dubail and A. Zahra)

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Date/Time : 28 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Koulik Khamaru, Rutgers University

Modern decision-making increasingly relies on adaptive experimentation, particularly in settings such as A/B testing, multi-armed bandits, and reinforcement learning. While these methods enable more efficient learning and allocation of resources, they fundamentally challenge traditional statistical inference. Classical i.i.d.-based tools often break down under adaptive data collection, resulting in biased estimators and misleading confidence intervals.

This talk offers an overview of statistical inference in these adaptive environments. We highlight the pitfalls of naive inference through concrete examples and introduce the concept of stability—originally formulated by Lai and Wei (1982)—as a unifying principle for valid inference under adaptivity. A key advantage of stability is that it allows us to recover classical inferential guarantees—such as asymptotic normality and valid confidence intervals—even when the data arise from highly adaptive algorithms. In other words, stability serves as the bridge that lets i.i.d.-based tools remain valid in non-i.i.d. bandit settings.

Next, we discuss the stability properties of two widely used algorithms: the Upper Confidence Bound (UCB) and Thompson Sampling. We argue that while UCB is stable, Thompson Sampling is not. Finally, we propose a modification of Thompson Sampling that regains stability while maintaining near-optimal regret. Key illustrations include quantitative central limit theorems of empirical mean in stochastic bandits and least square estimators in contextual bandits. We also present a new proof technique for analyzing regret and establishing stability, which we believe has broader applicability and may be of independent interest.

The talk is based on a series of joint works with Cunhui Zhang, Qiyang Han, Budhaditya Halder, Subhayan Pan, and Samya Praharaj.

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