相关论文: The Bouchaud-Anderson model with double-exponentia…
It is well-known that both branching random walk models and trap models can exhibit intermittency and localisation phenomena; the prototypical examples being the parabolic Anderson and Bouchaud trap models respectively. Our aim is to…
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. We prove that the model eventually localises on exactly two sites with overwhelming probability. This is a…
In this paper, we introduce a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent…
This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily large times…
We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in…
We study the stationary states of an over-damped active Brownian particle (ABP) in a harmonic trap in two dimensions, via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with…
The Periodic Anderson Model (PAM) can be studied in the infinite U limit by employing the Hubbard X operators to project out the unwanted states. We have already studied this problem employing the cumulant expansion with the hybridization…
We establish the exact quenched asymptotic growth of the solution to the parabolic Anderson model (PAM) in the hyperbolic space with a regular, stationary, time-independent Gaussian potential. More precisely, we show that with probability…
In this paper, we study a spatial model for dormancy in a random environment via a two-type branching random walk in continuous-time, where individuals switch between dormant and active states depending on the current state of a fluctuating…
We propose the Plaid Atoms Model (PAM), a novel Bayesian nonparametric model for grouped data. Founded on an idea of `atom skipping', PAM is part of a well-established category of models that generate dependent random distributions and…
We propose a new overarching model for self-propelled particles that flexibly generates a full family of "descendants". The general dynamics introduced in this paper, which we denote as "parental" active model (PAM), unifies two special…
In this paper, we study a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent of…
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…
We consider branching random walk in spatial random branching environment (BRWRE) in dimension one, as well as related differential equations: the Fisher-KPP equation with random branching and its linearized version, the parabolic Anderson…
Attributing a positive value \tau_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\tau_x), often known as "Bouchaud's trap model". We assume that these weights are…
We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently…
Anderson localization in a two-dimensional ultracold Bose-gas has been demonstrated experimentally. Atoms were released within a dumbbell-shaped optical trap, where the channel of variable aspect ratio provided the only path for particles…
We study the total mass of the solution to the parabolic Anderson model on a regular tree with an i.i.d. random potential whose marginal distribution is double-exponential. In earlier work we identified two terms in the asymptotic expansion…
Periodic Anderson model (PAM), where local electron orbitals interplay with itinerant electronic carriers, plays an essential role in our understanding on heavy fermion materials. Motivated by recent proposal of simulating Kondo lattice…
We discuss the physical consequences of a duality between two models with quenched disorder, in which particles propagate in one dimension among random traps or across random barriers. We derive an exact relation between their diffusion…