Related papers: Time-time covariance for last passage percolation …
In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $\LL^2$-formula relating the initial measure with the last-passage percolation time.…
We consider first-passage percolation on the two-dimensional integer lattice Z^2 with passage times that are IID exponentials of mean one. It has been conjectured, based on numerical evidence, that the variance of the time T(0,n) to reach…
We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By…
We consider the model of i.i.d. first passage percolation on $\mathbb{Z}^d$ : we associate with each edge $e$ of the graph a passage time $t(e)$ taking values in $[0,+\infty]$, such that $\mathbb{P}[t(e)<+\infty] >p_c(d)$. Equivalently, we…
In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions of a first-order ordinary differential equation with…
For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…
Consider the restriction of the directed landscape $\mathcal L(x, s; y, t)$ to a set of the form $\{x_1, \dots, x_k\} \times \{s_0\} \times \mathbb R \times \{t_0\}$. We show that on any such set, the directed landscape is given by a last…
We consider a model of long-range first-passage percolation on the $d$ dimensional square lattice $Z^d$ in which any two distinct vertices $x, y \in Z^d$ are connected by an edge having exponentially distributed passage time with mean…
In this paper we consider first passage percolation on the square lattice \(\mathbb{Z}^d\) with passage times that are independent and have bounded \(p^{th}\) moment for some \(p > 6(1+d),\) but not necessarily identically distributed. For…
We report on the first exact solution of the KPZ equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
We review recent progress on the study of the Kardar-Parisi-Zhang (KPZ) equation in a periodic setting, which describes the random growth of an interface in a cylindrical geometry. The main results include central limit theorems for the…
We establish higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic Cauchy problems accompanied with rapidly oscillating initial data. Such result is new even for linear problems. Here we construct…
The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
There are various models of first passage percolation (FPP) in $\mathbb R^d$. We want to start a very general study of this topic. To this end we generalize the first passage percolation model on the lattice $\mathbb Z^d$ to $\mathbb R^d$…
Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…
On the $Z^2$ lattice, vertices are assigned random weights $W(i,j)$. The point-to-point last passage percolation (LPP) time $S_{M,N+1-M}$ between $(1,1)$ and $(M,N+1-M)$ is the maximum total weight among all upward/right-oriented paths…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…