Related papers: Temporal Correlation in Last Passage Percolation w…
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. Stationary cocycles are constructed…
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 $\mathbb Z^2$ with independent and identically distributed weights whose common distribution is absolutely continuous with a finite exponential moment. Under the assumption that the limit shape has…
We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point…
In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the…
It is an open problem to show that in two-dimensional first-passage percolation, the sequence of finite geodesics from any point to $(n,0)$ has a limit in $n$. In this paper, we consider this question for first-passage percolation on a wide…
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 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…
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 consider i.i.d. last-passage percolation on $\mathbb{Z}^2$ with weights having distribution $F$ and time-constant $g_F$. We provide an explicit condition on the large deviation rate function for independent sums of $F$ that determines…
We prove the existence of semi-infinite geodesics for Brownian last-passage percolation (BLPP). Specifically, on a single event of probability one, there exist semi-infinite geodesics started from every space-time point and traveling in…
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 celebrate the 50th anniversary of one the most classical models in probability theory. In this survey, we describe the main results of first passage percolation, paying special attention to the recent burst of advances of the past 5…
We consider geodesics for first passage percolation (FPP) on $\mathbb{Z}^d$ with iid passage times. As has been common in the literature, we assume that the FPP system satisfies certain basic properties conjectured to be true, and derive…
The metric $D_\alpha (q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $R^d$, defined as the infimum of $(\sum_i |q_i - q_{i+1}|^\alpha)^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$…
This note establishes a universal directed landscape limit for last passage percolation models in an intermediate scaling regime. We find as a quick consequence the transversal fluctuations for geodesics taken near the axis. We extend the…
We consider directed random graphs, the prototype of which being the Barak-Erd\H{o}s graph $\vec G(\mathbb Z, p)$, and study the way that long (or heavy, if weights are present) paths grow. This is done by relating the graphs to certain…
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…
In this paper we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder of width $o(N^{2/3})$ and…
We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the increment-stationary variants of the model, and is presented in…