Related papers: A Geometric Perspective on First-Passage Competiti…
The emerging field of high-throughput compartmentalized in vitro evolution is a promising new approach to protein engineering. In these experiments, libraries of mutant genotypes are randomly distributed and expressed in microscopic…
We study the critical case of first-passage percolation in two dimensions. Letting $(t_e)$ be i.i.d. nonnegative weights assigned to the edges of $\mathbb{Z}^2$ with $\mathbb{P}(t_e=0)=1/2$, consider the induced pseudometric (passage time)…
As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function…
We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions,…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting,…
The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…
I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…
There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…
We study how stochastic resetting affects first-passage processes in systems of many interacting particles. While resetting is well understood for single-particle dynamics, its consequences for collective behavior remain less clear. We…
This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J. of Math. Biol. `18) where we have characterized the persistence…
We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding…
We study infection spread among biased random walks on $\mathbb{Z}^{d}$. The random walks move independently and an infected particle is placed at the origin at time zero. Infection spreads instantaneously when particles share the same site…
In multitype lattice gas models with hard-core interaction of Widom--Rowlinson type, there is a competition between the entropy due to the large number of types, and the positional energy and geometry resulting from the exclusion rule and…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
Consider the model where particles are initially distributed on $\mathbb{Z}^d, \, d\geq 2$, according to a Poisson point process of intensity $\lambda>0$, and are moving in continuous time as independent simple symmetric random walks. We…
The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…