Related papers: On some special directed last-passage percolation …
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
In this note, we prove convergence of the half-space exponential last passage percolation (LPP) model, away from the boundary, to the directed landscape. Our approach couples the half-space and full-space LPP models and constructs two…
We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…
Spatial L{\'{e}}vy-like flights are introduced as a way in the absorbing phase transitions to produce non-local interactions. We utilize the autoencoder, an unsupervised learning method, to predict the critical points for $(1+1)$-d directed…
We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical…
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…
We give an explicit formula for the joint density of the max and argmax of the Airy$_2$ process minus a parabola. The argmax has a universal distribution which governs the rescaled endpoint for large time or temperature of directed polymers…
We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process on $n$ particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic…
We study time reversal, last passage time, and $h$-transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to an arbitrary level and analyze the distribution of the…
In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to…
A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest…
A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in \cite{G} in the context of the contact process in continuous time. As discussed here, it also…
It is argued that some phase--transitions observed in models of non-equilibrium wetting phenomena are related to contact processes with long-range interactions. This is investigated by introducing a model where the activation rate of a site…
We establish limit theorems for the maxima and minima of Airy$_1$ and Airy$_2$ processes (denoted by $\mathcal{A}_1(\cdot)$ and $\mathcal{A}_2(\cdot)$ respectively) over growing intervals. In particular, we identify the finite non-zero…
In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function…
Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function $P(X,t)$ of packets of spreading random walkers, were observed in numerous situations…
We introduce and study a non-oriented first passage percolation model having a property of statistical invariance by time reversal. This model is defined in a graph having directed edges and the passage times associated with each set of…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…
We consider Fokker-Planck equations in the whole Euclidean space, driven by Levy processes, under the action of confining drifts, as in the classical Ornstein-Ulhenbeck model. We introduce a new PDE method to get exponential or…
We suggest an equal-time n-point correlation function for systems in the directed percolation universality class which is well defined in all phases and independent of initial conditions. It is defined as the probability that all points are…