相关论文: On the visibility window for Brownian interlacemen…

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…

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 study a dense colloidal suspension confined between two quasiparallel glass plates as a model system for a supercooled liquid in confined geometries. We directly observe the three-dimensional Brownian motion of the colloidal particles…

A recently discovered inverse correlation between QSO redshift and long-term continuum variability timescales was suggested to be the signature of microlensing on cosmological scales (Hawkins 1993). A general theoretical method for…

We consider a Brownian particle with diffusion coefficient $D$ in a $d$-dimensional ball of radius $R$ with reflecting boundaries. We study the maximum $M_x(t)$ of the trajectory of the particle along the $x$-direction at time $t$. In the…

The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…

We investigate the behavior of large connected components in the Poisson Random Connection model in non-critical regimes with any bounded connection function. We show that the asymptotic size of the largest component restricted to a window…

We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison…

In this paper we study the existence phase transition of scale invariant random fractal models. We determine the exact value of the critical point of this phase transition for all models satisfying some weak assumptions. In addition, we…

We study the one dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost ($X_{\max}\geq 0$) and leftmost ($X_{\min} \leq 0$) visited sites up to time $t$. At each time step the…

We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of $N$ particles is studied and it is described by use of the…

In a recent paper [S. Mandal et al., Phys. Rev. E 88, 022129 (2013)] the nature of spatial correlations of plasticity in hard sphere glasses was addressed both via computer simulations and in experiments. It was found that the…

We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the $N$-site fermion model are used to compute the entropy density:…

We study trajectories of d-dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential V can be associated to a field of traps whose centers location is given by a Poisson…

The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories,…

The entanglement entropy and quantum fidelity in a hard-core-boson model with nearest- and next-nearest-neighbor interactions are studied numerically. By using exact diagonalization and the density matrix renormalization group, the effects…

We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K $\subset$ R d with non empty interior. In a first setting, the Boolean model is a…

We consider a system of $N$ bosons where the particles experience a short range two-body interaction given by $N^{-1}v_N(x)=N^{3\beta-1}v(N^\beta x)$ where $v \in C^\infty_c(\mathbb{R}^3)$, without a definite sign on $v$. We extend the…

Characterising the statistical properties of classical interacting particle systems is a long-standing question. For Brownian particles the microscopic density obeys a stochastic evolution equation, known as the Dean--Kawasaki equation.…

We study the ionic distribution near a charged surface. A new method for performing Monte Carlo simulations in this geometry is discussed. A theory is then presented that allows us to accurately reproduce the density profiles obtained in…