Related papers: Criticality of a randomly-driven front
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
We study the asymptotic behaviour, in the small noise limit, of stochastic travelling wave solutions to reaction-diffusion equations perturbed by Wright-Fisher noise. Such equations are predicted to display three distinct responses to noise…
The infinite Atlas model describes the evolution of a countable collection of Brownian particles on the real line, where the lowest particle is given a drift of $\gamma \in [0,\infty)$. We study equilibrium fluctuations for the Atlas model…
Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…
Scaling and mechanism of the propagation speed of turbulent fronts in pipe flow with the Reynolds number has been a long-standing problem in the past decades. Here, we derive an explicit scaling law of the upstream front speed, which…
We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.…
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two…
We study the statistics, in stationary conditions, of the work $W_\tau$ done by the active force in different systems of self-propelled particles in a time $\tau$. We show the existence of a critical value $W_\tau ^\dag$ such that…
Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in i.i.d. random environment, $Z_{r,n}$ be the number of particles in the process at moment $0\leq r\leq n-1$ that have a positive number of descendants in generation…
We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a…
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particles being absorbed before some final time horizon, given the…
A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ yet the distribution of particle displacements is strongly…
We consider critical branching Brownian motion with absorption, in which there is initially a single particle at $x > 0$, particles move according to independent one-dimensional Brownian motions with the critical drift of $-\sqrt{2}$, and…
We use Brownian dynamics simulations of a binary mixture of highly charged spherical colloidal particles to illustrate many of the implications of the Random First Order Transition (RFOT) theory (PRA 40 1045 (1989)), which is the only…
We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site $n \ge 1$. Particles become active when hit by another active particle. Once activated, the particle…
Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching…
We study the shape of the outer envelope of a branching Brownian motion (BBM) in $\mathbb{R}^d$, $d\geq 2$. We focus on the extremal particles: those whose norm is within $O(1)$ of the maximal norm amongst the particles alive at time $t$.…
For the classical reaction diffusion equation, the priori speed of fronts is determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier, {\em Commun. Math. Phys.} 175:221--227, 1996) by variational characterization method.…
A granular system confined in a quasi two-dimensional box that is vertically vibrated can transit to an absorbing state in which all particles bounce vertically in phase with the box, with no horizontal motion. In principle, this state can…