The Triangle Probability Forum is a regular regional probability seminar for North Carolina’s Research Triangle. It is organized jointly by the probability groups of Duke University, North Carolina State University, and the University of North Carolina at Chapel Hill. Meetings are held twice each semester and rotate between the three universities. Afterwards, we have an informal social dinner together. Everyone is welcome to attend.
Announcements of upcoming seminars are sent to the probability seminar mailing lists at Duke, NC State, and UNC.
See Directions and parking for meeting locations and transportation information.
Spring 2026 meetings
Friday, February 27, 2026 at Duke
2:30pm: Tea in Physics 101
3:15pm in Physics 119: Paul Dupuis (Brown University)
Particle exchange Monte Carlo methods for eigenfunction and related nonlinear problems
Particle exchange methods such as parallel tempering are arguably the most effective computational tools for approximating integrals with respect to high-dimensional Gibbs measures with complex structure. One can consider the Gibbs measure as the solution to an eigenvalue/eigenfunction problem with known (zero) eigenvalue. In this talk we describe how these methods can be generalized to problems where the eigenvalue is not known a priori. However, to obtain an appropriate particle exchange rule one must replace a single particle by a pair of processes, with one evolving forward in time and the other backward. Applications to eigenfunction problems corresponding to quasistationary distributions and ergodic stochastic control are discussed. Joint work with Benjamin Zhang.
4:15pm in Physics 119: Michael Damron (Georgia Institute of Technology)
Percolation and first-passage percolation on logarithmic subsets of Z^2
In two-dimensional Bernoulli percolation, we declare each edge of the square grid Z^2 to be open with probability p or closed with probability 1-p, independently from edge to edge. There is a critical value p_c = 1/2, such that for p < p_c, all components of open edges are finite, and for p > p_c, there is a unique infinite component of open edges. In ’83, Grimmett introduced the following variant. Let f be a nonnegative real function on [0,\infty), and consider the subgraph G_f of Z^2 induced by the edges between the positive first coordinate axis and the graph of f. Grimmett found that if f(u) \sim a \log u as u \to \infty, the critical value p_c(f) for percolation on G_f equals a specific function of a only. In ’86, Chayes-Chayes considered the function f(u) = a \log(1+u) + b \log(1+\log(1+u)) and showed that if b > 2a, then the percolation G_f has an infinite open component at the critical point (i.e., a discontinuous phase transition). In joint work with Wai-Kit Lam, we prove that the phase transition is discontinuous if and only if b > a, and we compute sharp asymptotics for all p, a, and b of the expected passage time in G_f from the origin to the vertical line x=n in the related first-passage percolation model, improving results of Ahlberg. We also find asymptotics for the variance and a central limit theorem.
Friday, April 10, 2026 at NC State
Time TBA: Miki Racz (Northwestern)
Time TBA: Timo Seppäläinen (University of Wisconsin-Madison)
Previous meetings
Friday, November 14, 2025 at UNC
3pm: Tea in Hanes Lounge
3:30pm in Hanes 120: Evita Nestoridi (Stony Brook University)
Limit profiles for reversible Markov chains
A central question in Markov chain mixing is the occurrence of cutoff, a phenomenon according to which a Markov chain converges abruptly to the stationary measure. The focus of this talk is the limit profile of a Markov chain that exhibits cutoff, which captures the exact shape of the distance of the Markov chain from stationarity. We will discuss techniques for determining the limit profile and its continuity properties under appropriate conditions.
4:30pm in Hanes 120: Atilla Yilmaz (Temple University)
Homogenization of nonconvex Hamilton-Jacobi equations in stationary ergodic media
I will start with a self-contained introduction to the homogenization of inviscid (first-order) and viscous (second-order) Hamilton-Jacobi (HJ) equations in stationary ergodic media in any dimension and then give a survey of the classical works that are concerned with periodic media or convex Hamiltonians. Afterwards, I will drop both of these assumptions and outline the results obtained in the last decade that: (i) establish homogenization for inviscid HJ equations in one dimension; and (ii) provide counterexamples to homogenization in the inviscid and viscous cases in dimensions two and higher. Finally, I will present my recent joint work with Elena Kosygina in which we prove homogenization for viscous HJ equations in one dimension and also describe how the solution of this problem differs qualitatively from that of its inviscid counterpart
Friday, September 12, 2025 at Duke
2:30pm: Tea in Physics 101
3:15pm in Physics 119: Mark Sellke (Harvard University)
Algorithmic Thresholds and Spin Glass Theory
Mean field spin glasses are a family of random functions in high dimension. Originally developed to explore properties of disordered magnets, these models have found close connections to a broad range of problems in computer science, combinatorics, and statistics. Parisi’s theory of replica symmetry breaking predicts the global maximum value of these functions. In many setting, this has been rigorously confirmed by Talagrand and others. What about efficient algorithms? Namely, given a random high-dimensional optimization problem, can one efficiently compute an approximately optimal solution? What about sampling a uniformly random solution? I will review recent progress on this class of problems.
4:15pm in Physics 119: Lingfu Zhang (California Institute of Technology)
Aspects of KPZ universality: random metrics and growth processes
For the lattice Z^2 with i.i.d. positive weights on edges, the distance between two vertices is the minimum total weight over all connecting paths. This model, known as 2D first passage percolation (FPP), turns Z^2 into a random metric space. It also generates random growth processes, such as the spread of an epidemic, where edge weights represent infection times. The strong KPZ universality conjecture asserts that both the random metric and the induced growth processes have universal scaling limits: the directed landscape (DL) and the KPZ fixed point (KPZFP), respectively. The DL is a random “metric” on R^2, while the KPZFP is a continuous growth process that can be generated from the DL.
In this talk, I will describe a new complementary connection: the metric DL can be constructed from the KPZFP. This allows any convergence of growth processes to the KPZFP to be lifted to convergence of the associated random metrics to the DL, and I will present some such applications. Based on joint work with Dauvergne.
