Related papers: Local resetting in non-conserving zero-range proce…
We consider a model of a population with fixed size $N$, which is subjected to an unlimited supply of beneficial mutations at a constant rate $\mu_N$. Individuals with $k$ beneficial mutations have the fitness $(1+s_N)^k$. Each individual…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We introduce a novel migration process, the target process. This process is dual to the zero-range process (ZRP) in the sense that, while for the ZRP the rate of transfer of a particle only depends on the occupation of the departure site,…
We study a zero-range process with system-size dependent jump rates, which is known to exhibit a discontinuous condensation transition. Metastable homogeneous phases and condensed phases coexist in extended phase regions around the…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times…
We formulate a statistical-mechanical description of a recently introduced random planting model in which plants are represented by growing hard disks. Seedlings of negligible size are introduced at random positions in a field, grow at a…
Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…
First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here we study the interplay…
We study the relaxation of a Brownian particle with long range memory under confinement in one dimension. The particle diffuses in an arbitrary confining potential and resets at random times to previously visited positions, chosen with a…
Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit…
Biological systems often consist of a small number of constituents and are therefore inherently noisy. To function effectively, these systems must employ mechanisms to constrain the accumulation of noise. Such mechanisms have been…
We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We…
We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider in particular a…
We study a class of nonequilibrium lattice models on a ring where particles hop in a particular direction, from a site to one of its (say, right) nearest neighbours, with a rate that depends on the occupation of all the neighbouring sites…
The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We have…
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse,…
The inclusion process is a stochastic lattice gas, which is a natural bosonic counterpart of the well-studied exclusion process and has strong connections to models of heat conduction and applications in population genetics. Like the…
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced…
We consider a model of asexually reproducing individuals with random mutations and selection. The rate of mutations is proportional to the population size, $N$. The mutations may be either beneficial or deleterious. In a paper by Yu,…