相关论文: The Bouchaud-Anderson model with double-exponentia…
The $N$-particle branching Brownian motion ($N$-BBM) is a branching Markov process which describes the evolution of a population of particles undergoing reproduction and selection. It has attracted a lot of interest due to its relations to…
The use of high-dimensional data for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed…
We study a one dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the sub-diffusive phase. Our central…
We determine exactly the ground state of the one-dimensional periodic Anderson model (PAM) in the strong hybridization regime. In this regime, the low energy sector of the PAM maps into an effective Hamiltonian that has a ferromagnetic…
We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed the features of a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If $p \in (0,1/2)$ and $1-p$…
Online learning via Bayes' theorem allows new data to be continuously integrated into an agent's current beliefs. However, a naive application of Bayesian methods in non stationary environments leads to slow adaptation and results in state…
We study a variation of the trapping reaction, A+B->A, in which both the traps (A) and the particles (B) undergo diffusion, and the traps upon meeting react according to A+A->0 or A. This two-species reaction-diffusion system is known to…
We study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the…
We propose an elementary but effective approach to studying a general class of Poissonized tenable and balanced urns on two colors. We characterize the asymptotic behavior of the process via a partial differential equation that governs the…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…
The parabolic Anderson model on $\mathbb{Z}^d$ with i.i.d. potential is known to completely localise if the distribution of the potential is sufficiently heavy-tailed at infinity. In this paper we investigate a modification of the model in…
We study a $d$-dimensional branching Brownian motion (BBM) among Poissonian obstacles, where a random trap field in $\mathbb{R}^d$ is created via a Poisson point process. In the soft obstacle model, the trap field consists of a positive…
It was recently shown that wavepackets with skewed momentum distribution exhibit a boomerang-like dynamics in the Anderson model due to Anderson localization: after an initial ballistic motion, they make a U-turn and eventually come back to…
The one-dimensional propagation of waves in a bichromatic potential may be modeled by the Aubry-Andr\'e Hamiltonian. The latter presents a delocalization-localization transition, which has been observed in recent experiments using ultracold…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
We consider the quenched localisation of the Bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that for each $N \in \{2, 3, \ldots\}$ there exists a…
The periodic Anderson model (PAM) captures the essential physics of heavy fermion materials. Yet even for the paramagnetic metallic phase, a practicable many-body theory that can simultaneously handle all energy scales while respecting the…