Related papers: Critical behaviour of random walks
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…
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 the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…
In this PhD thesis, I investigate the properties of symmetry-breaking dynamical phase transitions that manifest in the fluctuations of time-integrated observables within classical systems. In particular, I analyze how these phase…
The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the…
We study a one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector. On encountering the reflector, at site x, the walker is reflected (with probability r) to x-1 and the reflector is…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
We numerically investigate collective ordering and disordering effects for vortices in type-II superconductors interacting with square and triangular substrate arrays under a dc drive that is slowly rotated with respect to the fixed…
We perform molecular dynamics simulation of a small number of particles in a box with periodic boundary conditions from a view point of chaotic dynamical systems. There is a transition at a critical energy E_c that each particle is confined…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…