Related papers: Escape from an attractor generated by recurrent ex…
The mixer chain on a graph G is the following Markov chain. Place tiles on the vertices of G, each tile labeled by its corresponding vertex. A "mixer" moves randomly on the graph, at each step either moving to a randomly chosen neighbor, or…
Synaptic interactions structure the phase space of the dynamics of neural circuits and constrain neural computation. Understanding how requires methods that handle those discrete interactions, yet few exist. Recently, it was discovered that…
We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large fluctuations. Specifically, this is achieved by…
This study deals with polymer looping, an important process in many chemical and biological systems. We investigate basic questions on the looping dynamics of a polymer under tension using the freely-jointed chain (FJC) model. Previous…
Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For…
The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for…
A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to…
A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
In the absence of inhibition, excitatory neuronal networks can alternate between bursts and interburst intervals (IBI), with heterogeneous length distributions. As this dynamic remains unclear, especially the durations of each epoch, we…
The persistent character of the motion of active particles gives rise to accumulation at boundaries. I investigate the problem of run-and-tumble swimmers confined in a 1D box with hard walls, reporting expressions for the particles…
We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a…
Using a time operator, we define a tunneling time for a particle going through a barrier. This tunneling time is the average of the phase time introduced by other authors. In addition to the delay time caused by the resonances over the…
Activated escape of a Brownian particle from the domain of attraction of a stable focus over a limit cycle exhibits non-Kramers behavior: it is non-Poissonian. When the attractor is moved closer to the boundary oscillations can be discerned…
Complex or hostile environments can sometimes inhibit the movement capabilities of diffusive particles or active swimmers, who may thus become stuck in fixed positions. This occurs, for example, in the adhesion of bacteria to surfaces at…
Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with…
Classical escape in 2D Hamiltonian systems with the mixed state has been studied numerically and analytically. The wide class of potentials with the mixed state is presented by polinomial potentials. In potentials, where the mixed state…
The survival problem for a diffusing particle moving among random traps is considered. We introduce a simple argument to derive the quenched asymptotics of the survival probability from the Lifshitz tail effect for the associated operator.…