Related papers: Last passage percolation in hierarchical environme…
A competition model on $\mathbb{Z}_+^{2}$ governed by directed last passage percolation is considered. A stochastic domination argument between subtrees of the last passage percolation is put forward.
We consider an interacting particle system on the lattice involving pushing and blocking interactions, called PushASEP, in the presence of a wall at the origin. We show that the invariant measure of this system is equal in distribution to a…
We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on $\mathbb{Z}^d$, $d\geq 2$, including discrete Gaussian free fields, Ginzburg-Landau $\nabla \phi$…
We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…
In this paper we explore first passage percolation (FPP) on the Erd\H{o}s-R\'enyi random graph $G_n(p_n)$, where each edge is given an independent exponential edge weight with rate 1. In the sparse regime, i.e., when $np_n\to \lambda>1,$ we…
The Kardar-Parisi-Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our…
In first-passage percolation (FPP), we let $(\tau_v)$ be i.i.d. nonnegative weights on the vertices of a graph and study the weight of the minimal path between distant vertices. If $F$ is the distribution function of $\tau_v$, there are…
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…
We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
The study of transversal fluctuation of the optimal path has been a crucial aspect of the Kadar-Parisi-Zhang (KPZ) universality class. In this paper, we establish a new probability lower bound, with optimal exponential order, for the rare…
We consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq0$ with the reflecting boundary at $x=0$. The interface is initially flat, $h(x,t=0)=0$. We focus on the…
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…
We study the model of Directed Polymers in Random Environment in 1+1 dimensions, where the distribution at a site has a tail which decays regularly polynomially with power \alpha, where \alpha \in (0,2). After proper scaling of temperature…
We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar-Parisi-Zhang (KPZ) dynamics. We find that particles tend to cluster together…
We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…
We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight…
Consider the short-time probability distribution $\mathcal{P}(H,t)$ of the one-point interface height difference $h(x=0,\tau=t)-h(x=0,\tau=0)=H$ of the stationary interface $h(x,\tau)$ described by the Kardar-Parisi-Zhang equation. It was…
It is not known (and even physicists disagree) whether first passage percolation (FPP) on $\mathbb{Z}^d$ has an upper critical dimension $d_c$, such that the fluctuation exponent $\chi=0$ in dimensions $d>d_c$. In part to facilitate study…
Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [Phys. Rev. Lett. 130, 147101 (2023)], we demonstrated that the correct critical behaviors…