Thursday, May 28, 2026
10:00 – 10:45 AM Luiz Renato Fontes, University of São Paulo
Random Walks in Markovian Dynamical Environments
We survey recent results on the asymptotics of continuous time random walks on Z^d with time inhomogeneous jump rates given by a decreasing function of an environment given by independent birth-and-death or house-of-cards processes. In particular, we look at diffusive behavior under sufficient ergodicity of the environment, and subdiffusivity under weaker ergodicity, null recurrence and transience. Joint work with Maicon Pinheiro, Pablo Gomes and Thomás Freud.
10:45 – 11:15 AM Morning Coffee Break
11:15 AM – 12:00 PM Reza Gheissari, Northwestern University
Phase Ordering in Low-Temperature Ising Dynamics
We consider the out-of-equilibrium behavior of Ising Glauber dynamics at low temperatures. It is well-known that in its low-temperature regime, the Ising Glauber dynamics takes an exponential time to equilibrate, due to a bottleneck between the mostly plus and mostly minus phases of the model. The question of phase ordering, studied in the physics literature since the 1960s on $\mathbb Z^2$, asks whether bias in the magnetization at initialization makes the system (quasi-)equilibrate to the plus phase rapidly. Fontes, Schonmann, Sidoravicius showed on $\mathbb Z^d$ the zero-temperature analogue that from a product initialization with sufficient bias towards plus, the dynamics quickly absorbs into the all-plus configuration. We will discuss progress on the positive temperature version of this question, joint with Allan Sly.
12:00 – 2:00 PM Lunch Break
2:00 – 2:45 PM Krishnamurthi Ravishankar, State University of New York at New Paltz
Convergence of a Drainage Network Model to the Brownian Net
We prove that Howard network with branching converges to the Brownian net. The proof follows the approach of the original Sun and Swart paper on the Brownian net with some of the ideas from the work of Etheridge etal on the convergence of Fleming-Viot model to the Brownian net. This is done by studying the dependency structures of the model.
2:45 - 3:00 PM Question time/Short break
3:00 – 3:45 PM Matteo Muccioni, National University of Singapore
Multiplicative Averages of Plancherel Random Partitions: Elliptic Functions, Phase Transitions, and Applications
We consider random integer partitions λ that follow the Poissonized Plancherel measure of parameter t². Using Riemann–Hilbert techniques, we establish the asymptotics of the multiplicative averages
Q(t,s)=E[ ∏_{i≥1} (1+e^{η(λ_i−i+1/2−s)})^{-1} ]
for fixed η>0 in the regime t→+∞ and s/t=O(1). We compute the large-t expansion of log Q(t,xt), expressing the rate function 𝓕(x)=−lim_{t→∞} t^{-2}log Q(t,xt) and the subsequent divergent and oscillatory contributions explicitly in terms of elliptic theta functions.
The associated equilibrium measure presents nontrivial saturated regions and undergoes two third-order phase transitions of different nature, which we describe. Applications include an explicit characterization of tail probabilities of the height function of the q-deformed polynuclear growth model, the edge of the positive-temperature discrete Bessel process, and asymptotics of radially symmetric solutions to the 2D Toda equation with step-like initial data.
3:45 – 4:15 PM Afternoon Coffee Break
4:15 – 5:00 PM Alberto Gandolfi, NYU Abu Dhabi
Signed FK Percolation and the Ising Spin Glass Transition
This talk presents a solution to the long-standing issue of identifying percolation equivalents to phase transitions in spin glasses by introducing signed FK percolation. With a suitable notion of connection, infinite signed FK percolation clusters come in paired companions, and phases are determined by asymmetrically assigning spins to the two infinite companions, provided they are distinguishable. We will discuss this phenomenon on tree-like graphs as well as d-dimensional lattices. This is a joint work with Chuck Newman and Dan Stein.