Related papers: Height Fluctuations of Random Lozenge Tilings Thro…

Using a connection between the $q$-oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area,…

We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…

We study the three-dimensional persistent random walk with drift. Then we develop a thermodynamic model that is based on this random walk without assuming the Boltzmann-Gibbs form for the equilibrium distribution. The simplicity of the…

In this note, we consider random walks in the quarter plane with arbitrary big jumps. We announce the extension to that class of models of the analytic approach of [G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter…

We study various models of random non-crossing configurations consisting of diagonals of convex polygons, and focus in particular on uniform dissections and non-crossing trees. For both these models, we prove convergence in distribution…

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result…

We consider random interlacements on Z^d, with d bigger or equal to 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of…

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…

In this paper we consider arbitrary hexagons on the triangular lattice with three arbitrary bowtie-shaped holes, whose centers form an equilateral triangle. The number of lozenge tilings of such general regions is not expected --- and…

We study a variant of the down-up and up-down walks over an $n$-partite simplicial complex, which we call expanderized higher order random walks -- where the sequence of updated coordinates correspond to the sequence of vertices visited by…

The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…

We consider dimer models on graphs which are bipartite, periodic and satisfy a geometric condition called {\em isoradiality}, defined in \cite{Kenyon3}. We show that the scaling limit of the height function of any such dimer model is…

We study the asymptotics of bounded lecture hall tableaux. Limit shapes form when the bounds of the lecture hall tableaux go to infinity linearly in the lengths of the partitions describing the large-scale shapes of these tableaux. We prove…

We study the motion of discrete interfaces driven by ferromagnetic interactions on the two-dimensional triangular lattice by coupling the Almgren, Taylor and Wang minimizing movements approach and a discrete-to-continuum analysis, as…

Famously, a $d$-dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if $d \in \{1,2\}$ but transient if $d \geq 3$. Once spatial homogeneity is…

We obtain new non-asymptotic tail bounds for the height of uniformly random trees with a given degree sequence, simply generated trees and conditioned Bienaym\'e trees (the family trees of branching processes), in the process settling three…

These notes were written for the mini-course "Extrema of log-correlated random variables: Principles and Examples" at the Introductory School held in January 2015 at the Centre International de Rencontres Math\'ematiques in Marseille. There…

We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional Law of Large Numbers for the position of the walker, properly…

We study a model of random walk on a fluctuating rough surface using the field-theoretic renormalization group (RG). The surface is modelled by the well-known Kardar--Parisi--Zhang (KPZ) stochastic equation while the random walk is…

Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected…