Related papers: Aging two-state process with L\'{e}vy walk and Bro…
In this paper we study the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) introduced in [4] by continuous time random walks on square lattices. The state space of BMVD contains a $2$-dimensional…
We study memory dependent binary-state dynamics, focusing on the noisy-voter model. This is a non-Markovian process if we consider the set of binary states of the population as the description variables, or Markovian if we incorporate…
We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation…
The voter model with memory-dependent dynamics is theoretically and numerically studied at the mean-field level. The `internal age', or time an individual spends holding the same state, is added to the set of binary states of the…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
In a two-state free probability space $(A, \phi, \psi)$, we define an algebraic two-state free Brownian motion to be a process with two-state freely independent increments whose two-state free cumulant generating function is quadratic. Note…
Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. To date, many theories for the prevalence of two-state kinetics have been…
Population dynamics of individuals undergoing birth and death and diffusing by short or long ranged twodimensional spatial excursions (Gaussian jumps or L\'{e}vy flights) is studied. Competitive interactions are considered in a global case,…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
We introduce a new class of stochastic partial differential equations (SPDEs) with seed bank modeling the spread of a beneficial allele in a spatial population where individuals may switch between an active and a dormant state.…
We study the late time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution…
We investigate collective behavior of a system of two-dimensional interacting Brownian particles in the hydrodynamic regime. By means of the Martin-Siggia-Rose-Jenssen-de Dominicis formalism, we built up a generating functional for…
Two-time correlations are a crucial tool to probe the dynamics of many-body systems. We use these correlation functions to study the dynamics of dissipative quantum systems. Extending the adiabatic elimination method, we show that the…
We study the dynamical steady-states of a monolayer of chemically active self-phoretic colloids as a function of packing fraction and self-propulsion speed by means of Brownian dynamics simulations. We focus on the case that a chemical…
In a variety of systems which exhibit aging, the two-time response function scales as $R(t,s)\approx s^{-1-a} f(t/s)$. We argue that dynamical scaling can be extended towards conformal invariance, obtaining thus the explicit form of the…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations…
The Steepest Entropy Ascent approach is considered and applied to few-state systems. When the Hamiltonian of the system is time dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact…
We study two Brownian particles in dimension $d=1$, diffusing under an interacting resetting mechanism to a fixed position. The particles are subject to a constant drift, which biases the Brownian particles toward each other. We derive the…