Related papers: The frog model with death revisited
Subdiffusive fractional equations are not structurally stable with respect to spatial perturbations to the anomalous exponent (Phys. Rev. E 85, 031132 (2012)). The question arises of applicability of these fractional equations to model real…
A key insight from statistical physics about spin systems on random graphs is the central role played by Gibbs measures on trees. We determine the local weak limit of the hardcore model on random regular graphs asymptotically until just…
We study branching random walks in random i.i.d. environment in $\Z^d, d \geq 1$. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience,…
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
We reconsider the model of the randomly pinned planar flux array (or the two-dimensional XY-model with random fields and no vortices) in extensive Monte Carlo simulations. We show that contrary to what has been reported recently [Phys.\…
This study examines the tree models of mildly dissipative diffeomorphisms on the disk $\D$. These models are one-dimensional dynamical systems with ergodic aperiodic data as well as some properties of the original dynamics. The focus of…
We prove that if T is a tree on n vertices wih maximum degree D and the edge probability p(n) satisfies: np>c*max{D*logn,n^{\epsilon}} for some constant \epsilon>0, then with high probability the random graph G(n,p) contains a copy of T.…
In this paper we study the recurrence and transience of the $\mathbb{Z}^d$-valued branching random walk in random environment indexed by a critical Bienaym\'e-Galton-Watson tree, conditioned to survive. The environment is made either of…
I present a simple numerical model based on iteratively updating subgroups of a population, individually modeled by nonnegative real numbers, by a constant decay factor; however, at each iteration, one group is selected to instead be…
In this paper we show that all infinite trees which have bounded coordination and whose surface is negligible with respect to the volume in the limit of large distances (so that they can be embedded in a finite-dimensional euclidean space)…
We introduce a dynamic random hypergraph model constructed from a bipartite graph. In this model, both vertex sets of the bipartite graph are generated by marked Poisson point processes. Vertices of both vertex sets are equipped with marks…
The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model…
We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from $\mathbb{Z}^2$ by replacing every edge by a sufficiently large, but fixed number of edges in…
We prove a conjecture by Bertoin that the multi-dimensional elephant random walk on $\mathbb{Z}^d$($d\geq 3$) is transient and the expected number of zeros is finite. We also provide some estimates on the rate of escape. In dimensions $d=…
In this paper we obtain precise asymptotics for certain families of graphs, namely circulant graphs and degenerating discrete tori. The asymptotics contain interesting constants from number theory among which some can be interpreted as…
The value of a continuous character evolving on a phylogenetic tree is commonly modelled as the location of a particle moving under one-dimensional Brownian motion with constant rate. The Brownian motion model is best suited to characters…
Using German forest health monitoring data we investigate the main drivers leading to tree mortality and the association between defoliation and mortality; in particular (a) whether defoliation is a proxy for other covariates (climate,…
In a recent Letter Bray and Blythe have shown that the survival probability P(t) of an A particle diffusing with a diffusion coefficient D_A in a 1D system with diffusive traps B is independent of D_A in the asymptotic limit t \to \infty…
Under certain circumstances, a swarm of a species of trail-laying ants known as army ants can become caught in a doomed revolving motion known as the death spiral, in which each ant follows the one in front of it in a never-ending loop…