Related papers: Geodesic Forests in the Last-Passage Percolation
Consider the following partial "sorting algorithm" on permutations: take the first entry of the permutation in one-line notation and insert it into the position of its own value. Continue until the first entry is 1. This process imposes a…
We investigate extended processes given by last-passage times in directed models defined using exponential variables with decaying mean. In certain cases we find the universal Airy process, but other cases lead to non-universal and trivial…
In last passage percolation models lying in the Kardar-Parisi-Zhang universality class, maximizing paths that travel over distances of order $n$ accrue energy that fluctuates on scale $n^{1/3}$; and these paths deviate from the linear…
We introduce and study a model of directed last-passage percolation in planar layered environment. This environment is represented by an array of random exponential clocks arranged in blocks, for each block the average waiting times depend…
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…
We investigate first-passage percolation on the lattice $\Z^d$ for dimensions $d \geq 2$. Each edge $e$ of the graph is assigned an independent copy of a non-negative random variable $\tau$. We only assume $\P[\tau=0]0$ is explicit) for the…
In this article, we prove an extreme value theorem on the limit distribution of geodesics in a geometrically finite quotient of $\Gamma\backslash\mathcal{T}$ a locally finite tree. Main examples of such graphs are quotients of a Bruhat-Tits…
The hierarchical system of forest ecosystem models based on the theory of individual-based (structured) models of populations and communities is briefly described. New self-thinning models are integrated with tree stand models within a…
We propose a model for evolution aiming to reproduce statistical features of fossil data, in particular the distributions of extinction events, the distribution of species per genus and the distribution of lifetimes, all of which are known…
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior,…
We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice ${\mathbb Z}^d$ $(d\geq2)$ in which weights take finitely many values is typically exponentially large.
We consider directed first-passage and last-passage percolation on the nonnegative lattice Z_+^d, d\geq2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits…
For directed Bernoulli last passage percolation with i.i.d.~weights on vertices over a $n\times n$ grid and for $n$ large enough, the geodesics are shown to be concentrated in a cylinder, centered on the main diagonal and of width of order…
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,…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
Consider first passage percolation on $\mathbb{Z}^d$ with passage times given by i.i.d. random variables with common distribution $F$. Let $t_\pi(u,v)$ be the time from $u$ to $v$ for a path $\pi$ and $t(u,v)$ the minimal time among all…
We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding universe. We carefully evaluate and avoid numerical contamination in…
We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show that this version is both a bijection and an isometry, two…
We study Busemann functions, semi-infinite geodesics, and competition interfaces in the exactly solvable last-passage percolation with inhomogeneous exponential weights. New phenomena concerning geodesics arise due to inhomogeneity. These…