University of Victoria

Cooperative motion is a random walk process where the jump rate of a particle depends on the likelihood that another independent identical walker is at the same position. It was studied on the line in a paper by Addario-Berry, Cairns, Devroye...

Given two trees, what is the size and structure of their largest common shared subtree? This question has been a growing topic of interest in the probability/combinatorics community in recent years, with the problem having been discussed for a few...

Given a connected finite graph $G$, an integer-valued function $f$ on $V(G)$ is called $M$-Lipschitz if the value of $f$ changes by at most $M$ along the edges of $G$. In 2013, Peled, Samotij, and Yehudayoff showed that random $M$-Lipschitz functions...

In this talk, I shall present a unifying approach to study the replica-symmetric regime of general dilute spin glasses. In particular, we identify two regimes - high temperature and subcritical dilution - where we observe a large class of popular...

In this talk we will address the relatively new objects quaternary Legendre pairs. These objects (and their binary counterparts) were introduced in order to construct Hadamard matrices and have garnered renewed interest recently. Over the course of...

In recent years, harmonic analysts and fractal geometers have become increasingly interested in Ramsey-theoretic problems for subsets of Rn. Many of these were inspired by discrete analogues. Over the past 20 years, classical theorems from discrete...

Much of the recent rigorous progress on the classical Ising model was driven by new detailed understanding of its stochastic geometric representations. Motivated by the problem of establishing exponential decay of truncated correlations of the...

Site percolation models are probability distributions of 2-colorings of the vertices of locally finite infinite graphs. Historically, they have been studied on graphs exhibiting symmetries such as (quasi)-transitivity. In joint work with Alexander...

Defined as the difference between its two largest eigenvalues, the spectral gap of a graph plays an important role on our understanding of its connectivity as observed by Godsil and Royle (2001). Since computing the largest eigenvalue of a graph is...

We will introduce Random Spanning Trees in Random Environment (RSTRE), a disordered system on spanning trees that interpolates between the Uniform Spanning Tree (UST) and Minimum Spanning Tree (MST) measures. Our primary goal is to study how local...