Related papers: Strongly self-interacting processes on the circle
The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the "hockey-stick" upward trend of human technological evolution, where an explosion in the number of produced items with…
We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. L\'{e}vy processes endowed with rank-dependent drift and diffusion coefficients. In…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
Sufficient conditions for a symmetric jump-diffusion process to be conservative and recurrent are given in terms of the volume of the state space and the jump kernel of the process. A number of examples are presented to illustrate the…
The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
In this work, we focus on the behavior of a single passive Brownian particle in a suspension of passive particles with short-range repulsive interactions and a larger self-diffusion coefficient. While the forces affecting the…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…
Recent experimental results indicate that mixing is enhanced by a reciprocal flow induced inside a levitated droplet with an oscillatory deformation [T. Watanabe et al. Sci. Rep. 8, 10221 (2018)]. Generally, reciprocal flow cannot convect…
The purpose of this article is to study the hydrodynamic limit of the symmetric exclusion process with long jumps and in contact with infinitely extended reservoirs for a particular critical regime. The jumps are given in terms of a…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an…
A $d$-dimensional branching diffusion, $Z$, is investigated, where the linear attraction or repulsion between particles is competing with an Ornstein-Uhlenbeck drift, with parameter $b$ (we take $b>0$ for inward O-U and $b<0$ for outward…
There is currently a strong interest in the collective behavior of chiral active particles that can propel and rotate themselves. In the presence of alignment interactions for many chiral particles, chiral self-propulsion can induce vortex…
Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in…
Modelling diffusion processes on dynamic contact networks is an important research area for epidemiology, marketing, cybersecurity, and ecology. However, current diffusion models cannot capture transmissions occurring for indirect…
In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…