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We apply macroscopic fluctuation theory to study the diffusion of a tracer in a one-dimensional interacting particle system with excluded mutual passage, known as single-file diffusion. In the case of Brownian point particles with hard-core…
We study the probability of stability of a large complex system of size $N$ within the framework of a generalized May model, which assumes a linear dynamics of each population size $n_i$ (with respect to its equilibrium value): $…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme…
We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
The area enclosed by the two-dimensional Brownian motion in the plane was studied by L\'evy, who found the characteristic function and probability density of this random variable. For other planar processes, in particular ergodic diffusions…
We study the large distance behavior of a steady distribution of two Brownian particles under external driving in a two-dimensional space. Employing a method of perturbative system reduction, we analyze a Fokker-Planck equation that…
Suppose that $N_0$ independently diffusing particles, each with diffusivity $D$, are initially released at $x=\ell>0$ on the semi-infinite interval $0\leq x<\infty$ with an absorber at $x=0$. We determine the probability ${\cal P}(N)$ that…
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…
We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle etc.), that is confined by an external potential. Focusing on the limit in…
The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a…
Motivated by the wide range of applicability of the fluctuation and dissipation phenomena in non-equilibrium systems, we provide a universal study scheme for the dissipation of the energy and the corresponding Brownian motion analysis of…
We study random transitions between two metastable states that appear below a critical temperature in a one dimensional self-gravitating Brownian gas with a modified Poisson equation experiencing a second order phase transition from a…
We consider a branching Brownian motion in $\mathbb{R}^2$ in which particles independently diffuse as standard Brownian motions and branch at an inhomogeneous rate $b(\theta)$ which depends only on the angle $\theta$ of the particle. We…
The fluctuation-dissipation theorem describes the intimate connection between the Brownian diffusion of thermal particles and their drag coefficients. In the simple case of spherical particles, it takes the form of the Stokes-Einstein…
In computer simulations performed in constant number of particles ensembles, although the total number of particles N contained in the simulation box does not fluctuate, hence giving a zero apparent compressibility, there are still local…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…