Related papers: Determinantal Expressions in Multi-Species TASEP
Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. It has previously been shown that if the random environment is translational invariant, then the averaged…
The extremal tail probabilities of moving sums in a marked Poisson random field is examined here. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. Change of measure…
We show that the spectrum of an ensemble of two-level systems can be broadened through `resetting' discrete fluctuations, in contrast to the well-known motional-narrowing effect. We establish that the condition for the onset of motional…
We consider a two-speed branching random walk, which consists of two macroscopic stages with different reproduction laws. We prove that the centered maximum converges in law to a Gumbel variable with a random shift and the extremal process…
We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate that provides a stochastic changing of lengthes by a free diffusion law. The birth and death rates are length dependent which…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
The PASEP (Partially Asymmetric Simple Exclusion Process) is a probabilistic model of moving particles, which is of great interest in combinatorics, since it appeared that its partition function counts some tableaux. These tableaux have…
Dynamics of a system that performs a large fluctuation to a given state is essentially deterministic: the distribution of fluctuational paths peaks sharply at a certain optimal path along which the system is most likely to move. For the…
Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The…
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
We consider the totally asymmetric simple exclusion process with \emph{soft-shock} initial particle density, which is a step function increasing in the direction of flow and the step size chosen small to admit KPZ scaling. The initial…
We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we…
An analytic theory of species abundance patterns (SAPs) in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies interactions. Various…
The purpose of this work is to build a framework that allows for an in-depth study of various generalisations to inhomogeneous space of models of Borodin-Ferrari, Dieker-Warren, Nordenstam, Warren-Windridge of interacting particles in…
We determine the limiting distribution and the explicit tail behavior for the maximal displacement of a branching symmetric stable process with spatially inhomogeneous branching structure. Here the branching rate is a Kato class measure…
The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models verify Palis' conjecture: the long-term behavior is…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…