Related papers: The Cusp-Airy Process
We study analytically the Ising model coupled to random lattices in dimension three and higher. The family of random lattices we use is generated by the large N limit of a colored tensor model generalizing the two-matrix model for Ising…
In this paper, we study the asymptotic behavior of the first, second, and so on rows of stochastically decaying partitions. We establish that, with appropriate scaling in time and length, the sequence of rows converges to the Airy$_2$ line…
We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of…
The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a…
A coarsened model for a binary system with limited miscibility of components is proposed; the system is described in terms of structural states in small parts of the material. The material is assumed to have two alternative types of…
Phase transitions of systems confined in long cylindrical pores (capillary condensation, wetting, crystallization, etc.) are intrinsically not sharply defined but rounded. The finite size of the cross section causes destruction of long…
We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal…
For the stochastic six-vertex model on the quadrant $\mathbb{Z}_{\geq0}\times\mathbb{Z}_{\geq0}$ with step initial conditions and a single second-class particle at the origin, we show almost sure convergence of the speed of the second-class…
We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…
We study some asymptotic properties of cylinder processes in the plane defined as union sets of dilated straight lines (appearing as mutually overlapping infinitely long strips) derived from a stationary independently marked point process…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…
The Airy$_\beta$ point process, originally introduced by Ram\'irez, Rider, and Vir\'ag, is defined as the spectrum of the stochastic Airy operator $\mathcal{H}_\beta$ acting on a subspace of $L^2[0,\infty)$ with Dirichlet boundary…
In this work we have tried to study the interesting dynamics of Airy pulse under phase modulation. We investigate the role of linear, quadratic and cubic phase modulation on Airy pulse dynamics in pure linear regime. As a specific example,…
Let $\aip(t)$ be the Airy$_2$ process. We show that the random variable [\sup_{t\leq\alpha}\{aip(t)-t^2}+\min{0,\alpha}^2] has the same distribution as the one-point marginal of the Airy$_{2\to1}$ process at time $\alpha$. These marginals…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We consider a discrete polynuclear growth (PNG) process and prove a functioal limit theorem for its convergrence to the Airy process. This generalizes previous results by Pr"ahofer and Spohn. The result enables us to express the GOE largest…
We study linear statistics of a class of determinantal processes which interpolate between Poisson and GUE/Ginibre statistics in dimension 1 or 2. These processes are obtained by performing an independent Bernoulli percolation on the…
We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point on the arctic boundary, that is not a cusp or tangency…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a…