相关论文: Predator-prey dynamics on infinite trees: a branch…
We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
Consider a discrete-time supercritical discounted branching random walk, in which increments at depth $k$ are independent and identically distributed with the same law as $m^{-kH}Y$, where $Y$ has a fixed law, $H>0$, and $m>1$ is the…
This study introduces an innovative framework for merging ecological and epidemiological modeling via the formulation of a sophisticated predator-prey model that addresses the intricacies of disease dynamics, the Allee effect, and defensive…
We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying…
We introduce a model of branching interlacements for general critical offspring distributions. It consists of a countable collection of infinite tree-indexed random walk trajectories on $Z^d,d\geq5$. We show that this model turns out to be…
We introduce a model for the evolution of species triggered by generation of novel features and exhaustive combination with other available traits. Under the assumption that innovations are rare, we obtain a bursty branching process of…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
We study a family of Crump--Mode--Jagers branching processes in random environment that explode, i.e. that grow infinitely large in finite time with positive probability. Building on recent work of the author and Iyer (``On the structure of…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
Apparent competition is an indirect interaction between species that share natural resources without any mutual aggression but negatively affect each other if there is a common enemy. The negative results of the apparent competition are…
We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
Demographic data and recent experiments verify earlier predictions that mortality has short (few percent of the life span) memory of the previous life history, may be significantly decreased, reset to its value at a much younger age, and…
We study the extremes of branching random walks under the assumption that the underlying Galton-Watson tree has infinite progeny mean. It is assumed that the displacements are either regularly varying or they have lighter tails. In the…
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…