Related papers: Strongly self-interacting processes on the circle
We study certain self-interacting walks on the set of integers, that choose to jump to the right or to the left randomly but influenced by the number of times they have previously jumped along the edges in the finite neighbourhood of their…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
Depending on their mechanism of self-propulsion, active particles can exhibit a time-dependent, often periodic, propulsion velocity. The precise propulsion velocity profile determines their mean square displacement and their effective…
The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…
This paper deals with some self-interacting diffusions $(X_t,t\geq 0)$ living on $\mathbb{R}^d$. These diffusions are solutions to stochastic differential equations: \[\mathrm{d}X_t=\mathrm{d}B_t-g(t)\nabla…
We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…
By combining aspects of the coherent and self intermediate scattering functions, measured by dynamical light scattering on a suspension of hard sphere-like particles, we show that the arrest of particle number density fluctuations spreads…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
This paper studies regularity property of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly `infinite-activity'…
Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated…
By extracting unstable invariant solutions directly from body-forced three-dimensional turbulence, we study the dynamical processes at play when the forcing is large scale and either unidirectional in the momentum or the vorticity…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
A fluid motion through the flow element is presented in the kind of an autooscillating system with the distributed parameters: mass, elasticity, viscosity. The system contains a self-excited oscillator and possesses a self-regulation on…
Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this…
The long-time dynamics of reaction-diffusion processes in low dimensions is dominated by fluctuation effects. The one-dimensional coagulation-diffusion process describes the kinetics of particles which freely hop between the sites of a…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…