Related papers: The Brownian Castle
We study a simple one-dimensional model of ballisticaly-controlled annihilation in which the two annihilating species are initially spatially separated. The time dependent properties of the annihilation front are exactly derived. It is…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
We study metastable behaviour in systems of weakly interacting Brownian particles with localised, attractive potentials which are smooth and globally bounded. In this particular setting, numerical evidence suggests that the particles…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and…
It was recently shown [Phys. Rev. Lett. {\bf 110}, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming…
We present a study of diffusion enhancement of underdamped Brownian particles in 1D symmetric space-periodic potential due to external symmetric time-periodic forcing with zero mean. We show that the diffusivity can be enhanced by many…
The spontaneous localization mechanism of collapse models induces a Brownian motion in all physical systems. This effect is very weak, but experimental progress in creating ultracold atomic systems can be used to detect it. In this paper,…
Theoretically, we recently showed that the scaling relation between the transition temperature T_c and the superfluid density at zero temperature n_s (0) might exhibit a parabolic pattern [Scientific Reports 6 (2016) 23863]. It is…
We study stationary fluctuations in two models involving $N$ Brownian particles undergoing stochastic resetting to the origin in 1d. We start with the basic reset model where the particles reset independently (model A). Then we introduce…
We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. In the case of quarter filling, we show the uniqueness of the…
We derive a general quantum formula giving the mean-square displacement of a diffusing particle as a function of time. Near {\bf 0 K} we find a universal logarithmic behavior (valid for times longer than the relaxation time), and deviations…
We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position…
In this paper the three dimensional random field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the…
We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate $r$…
Stochastically gated interfaces play an important role in a variety of cellular diffusion processes. Examples include intracellular transport via stochastically gated ion channels and pores in the plasma membrane of a cell, intercellular…
This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the $n$-th Brownian motion is reflected from the Brownian motion with label $n-1$. This model belongs…
The "Brownian bees" model describes a system of $N$ independent branching Brownian particles. At each branching event the particle farthest from the origin is removed, so that the number of particles remains constant at all times.…
The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on…
This text considers the discrete height functions associated with the Berezinskii--Kosterlitz--Thouless transition (BKT) at slope zero. Our main results are as follows. * Sharpness: If the model is localised, then the two-point function…