Related papers: To fixate or not to fixate in two-type annihilatin…
We consider a supercritical branching random walk in time-inhomogeneous random environment with a random absorption barrier, i.e.,in each generation, only the individuals born below the barrier can survive and reproduce. Assume that the…
We study a competitive stochastic growth model called chase-escape in which red particles spread to adjacent uncolored sites and blue only to adjacent red sites. Red particles are killed when blue occupies the same site. If blue has rate-1…
We study the the survival probability P(t) upto time t, of a test particle moving in a fluctuating external field. The particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field…
We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…
In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…
We study a system of interacting urns where balls of different colour/type compete for their survival, and annihilate upon contact. For competition between two types, the underlying graph (finite and connected), determining the interaction…
For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set.…
Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in $R^d$. For a positive (respectively, negative) parameter $\gamma$ we consider red-blue matchings that locally minimize (respectively,…
In this paper we consider an irreducible random walk on the integer lattice $\mathbb{Z}$ that is in the domain of normal attraction of a strictly stable process with index $\alpha\in (1, 2)$ and obtain the asymptotic form of the…
One of the most striking effect of fluctuations in evolutionary game theory is the possibility for mutants to fixate (take over) an entire population. Here, we generalize a recent WKB-based theory to study fixation in evolutionary games…
We consider two-player games played on finite colored graphs where the goal is the construction of an infinite path with one of the following frequency-related properties: (i) all colors occur with the same asymptotic frequency, (ii) there…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
Suppose that red and blue points occur as independent homogeneous Poisson processes in R^d. We investigate translation-invariant schemes for perfectly matching the red points to the blue points. For any such scheme in dimensions d=1,2, the…
We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random…
We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition…
We prove an almost sure invariance principle for a random walker among i.i.d. conductances in $\Z^d$, $d\geq 2$. We assume conductances are bounded from above but we dot require they are bounded from below.
We consider $d$ independent walkers in the same random environment in $\mathbb{Z}$. Our assumption on the law of the environment is such that a single walker is transient to the right but subballistic. We show that - no matter what $d$ is -…
We prove a quenched invariance principle for a class of random walks in random environment on $\mathbb{Z}^d$, where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the…
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation…
For a highly beneficial mutant $A$ entering a randomly reproducing population of constant size, we study the situation when a second beneficial mutant $B$ arises before $A$ has fixed. If the selection coefficient of $B$ is greater than the…