Related papers: Stationary half-space last passage percolation
We investigate properties of two-dimensional finite-scale percolation systems whose size along the current flow is smaller than the perpendicular size. Successive thresholds of appearing multiple percolation channels in such systems have…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
For exactly solvable models of planar last passage percolation, it is known that geodesics of length $n$ exhibit transversal fluctuations at scale $n^{2/3}$ and matching (up to exponents) upper and lower bounds for the tail probabilities…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled coordinates may be introduced, so that these…
Density fluctuations in the matter distribution lead to distortions of the images of distant galaxies through weak gravitational lensing effects. This provides an efficient probe of the cosmological parameters and of the density field. In…
We extend the random walk framework to include compounded steps, providing first-passage time (FPT) properties for a new class of superdiffusive processes, which are governed by the space-fractional spectral Fokker-Planck equation. This…
Let $\{\eta_{N, v}: v\in V_N\}$ be a discrete Gaussian free field in a two-dimensional box $V_N$ of side length $N$ with Dirichlet boundary conditions. We study the Liouville first passage percolation, i.e., the shortest path metric where…
Discrete and continuum Liouville first passage percolation (DLFPP, LFPP) are two approximations of the conjectural $\gamma$-Liouville quantum gravity (LQG) metric, obtained by exponentiating the discrete Gaussian free field (GFF) and the…
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…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
In exponential last passage percolation, we consider the rescaled Busemann process $x\mapsto N^{-1/3}B^\rho_{0,[xN^{2/3}]e_1} \,\, (x\in\mathbb{R})$, as a process parametrized by the scaled density $\rho=1/2+\frac{\mu}{4} N^{-1/3}$, and…
We investigate the \emph{last passage percolation} problem on transitive tournaments, in the case when the edge weights are independent Bernoulli random variables. Given a transitive tournament on $n$ nodes with random weights on its edges,…
The fluctuations of the passage time in first passage percolation are of great interest. We show that the non-random fluctuations in planar FPP are at least of order $\log(n)^\alpha$ for any $\alpha<1/2$ under some conditions that are known…
We show that the Radon-Nikodym derivative of the law of the spatial increments (with endpoints away from the origin) of inhomogeneous Brownian last passage percolation (LPP) with non-decreasing initial data against the Wiener measure $\mu$…
The energy and geometry of maximizing paths in integrable last passage percolation models are governed by the characteristic KPZ scaling exponents of one-third and two-thirds. When represented in scaled coordinates that respect these…
We study a family of reaction-diffusion equations that present a doubly nonlinear character given by a combination of the $p$-Laplacian and the porous medium operators. We consider the so-called slow diffusion regime, corresponding to a…
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…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
In this paper we consider first-passage percolation on certain 1-dimensional periodic graphs, such as the $\Z\times\{0,1,\ldots,K-1\}^{d-1}$ nearest neighbour graph for $d,K\geq1$. We find that both length and weight of minimal-weight paths…