Date/Time : 23 Oct 2026 09:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Yaolin Yu, Fudan University

This talk gives an introduction to continuous stochastic flows driven by space-time white noise (arXiv:2606.12143) and discusses two applications. The first addresses open questions about local time flows associated with skew Brownian motion by exploring their connection with squared Bessel flows (arXiv:2411.04773). The second constructs polynomially self-repelling motion (PSRM) via PSR flows as the scaling limit of polynomially self-repelling walks. This ongoing work shows that the limit differs from the Brownian motion perturbed at its extrema (BMPE) conjectured by Tóth in the 1990s.

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Date/Time : 23 Oct 2026 10:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ruibo Kou, Warwick University

We introduce and study a one-dimensional singular birth-death model constructed from Itô’s Brownian excursion measure. In this model, particles are born at the origin at infinite rate, evolve as Brownian excursions away from the origin, and are killed upon returning to the origin. Although the number of particles alive at any fixed deterministic time is almost surely finite, we prove that the set of exceptional times at which infinitely many particles are alive is almost surely dense and has Hausdorff dimension 1/2. We further investigate the spatial structure of the particle system at such exceptional times. In particular, we identify the critical near-origin profile of the infinite particle cloud, which is governed by a scale of order loglog(1/|x|)^{−1} as x \to 0. Finally, we establish laws of large numbers and central limit theorems for the top particle position.

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Date/Time : 23 Oct 2026 10:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Zian Li, Shandong University

We consider a pinning model in correlated Gaussian random environments. For the model that is disorder relevant, we show that the rescaled partition functions converge to a non-trivial continuum limit in the Skorohod setting and in the Stratonovich setting, respectively. Our results partially confirm the Weinrib and Halperin prediction for disorder relevance/irrelevance.

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Date/Time : 23 Oct 2026 11:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Hang Zhang, Shandong University

I will talk about a fractional stochastic heat equation motivated by the disordered pinning model. Inspired by the work of Quastel, Ramírez, and Virág, we construct a unique global, strictly positive solution in a suitable parameter regime. This solution is genuinely L^1: it does not belong to L^p for any p>1. We also discuss the connection with the Weinrib–Halperin prediction for disorder relevance. This talk is based on joint work with Zi’an Li, Jian Song, and Ran Wei.

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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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