Related papers: Limit shape formulas for a generalized Sepp\"al\"a…
Let $\{X(v), v \in \Bbb Z^d \times \Bbb Z_+\}$ be an i.i.d. family of random variables such that $P\{X(v)= e^b\}=1-P\{X(v)= 1\} = p$ for some $b>0$. We consider paths $\pi \subset \Bbb Z^d \times \Bbb Z_+$ starting at the origin and with…
A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
We survey some results and applications of last percolation models of which the limiting distribution can be evaluated.
We generalize the exactly solvable corner growth models by choosing the rate of the exponential distribution $a_i+b_j$ and the parameter of the geometric distribution $a_i b_j$ at site $(i, j)$, where $(a_i)_{i \ge 1}$ and $(b_j)_{j \ge 1}$…
We study the facilitated totally asymmetric exclusion process on the one dimensional integer lattice. We investigate the invariant measures and the limiting behavior of the process. We mainly derive the limiting distribution of the process…
We consider the exponential last passage percolation (LPP) with thick two-sided boundary that consists of a few inhomogeneous columns and rows. Ben Arous and Corwin previously studied the limit fluctuations in this model except in a…
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency…
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
In this paper we show weak convergence of the empirical eigenvalue distribution and of the weighted spectral measure of the Jacobi ensemble, when one or both parameters grow faster than the dimension $n$. In these cases the limit measure is…
We consider the standard first passage percolation model in $\mathbb{Z}^d$ for $d\geq 2$. We are interested in two quantities, the maximal flow $\tau$ between the lower half and the upper half of the box, and the maximal flow $\phi$ between…
This article is concerned with the derivation of the Gauss-Codazzi's constraints equations on the initial light cone for geometric transport equations in general relativity. Temporal-gauge-dependent constraints are addressed too and…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
We survey recent results on first-passage processes in unbounded cones and their applications to ordering of particles undergoing Brownian motion in one dimension. We first discuss the survival probability S(t) that a diffusing particle, in…
The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli \rho measure as initial conditions, 0<\rho<1, is stationary in space and time. Let N_t(j) be the number of particles which have…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
We study a geometric version of first-passage percolation on the complete graph, known as long-range first-passage percolation. Here, the vertices of the complete graph $\mathcal K_n$ are embedded in the $d$-dimensional torus $\mathbb…
We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density rho_- and right density rho_+. We consider the associated height function, whose discrete gradient is…
We develop a fully analytical waveform model for precessing binaries with arbitrary spin vectors using post-Newtonian~(PN) theory in the extreme mass-ratio limit and a hierarchical multi-scale analysis. The analytical model incorporates…
We show quenched large deviations for the simple random walk on a certain class of percolations with long-range correlations. This class contains the supercritical Bernoulli percolations, the model considered by Drewitz, R'ath and…