arXiv subjects

Suney Toste

Publications and source records attributed to Suney Toste.

4 recordsLinked to original sources

arXiv2022

How large should be the redundant numbers of copy to make a rare event probable

The redundancy principle provides the framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. But what is $n$ large? To estimate large $n$ with respect to the geometrical properties of a domain and the dynamics, we present here a criteria based on splitting probabilities between a small fraction of the exploration space associated to an activation process and other absorbing regions where trajectories can be terminated. We obtain explicit computations especially when there is a killing region located inside the domain that we compare with stochastic simulations. We present also examples of extreme trajectories with killing in dimension 2. For a large $n$, the optimal trajectories avoid penetrating inside the killing region. Finally we discuss some applications to cell biology.

cond-mat.soft↗

arXiv2022

Extreme diffusion with point-sink killing field

We study here the escape time for the fastest diffusing particle from the boundary of an interval with point-sink killing sources. Killing represents a degradation that leads to the probabilistic removal of the moving Brownian particles. We compute asymptotically the mean time it takes for the fastest particle escaping alive and obtain the extreme statistic distribution. These computations relies on an explicit expression for the time dependent flux of the Fokker-Planck equation using the time dependent Green's function and Duhamel's formula. We obtain a general formula for several point-sink killing, showing how they directly interact. The range of validity of the present formula for the mean extreme times of the fastest is evaluated with Brownian simulations. Finally, we discuss some applications to the early calcium signaling at neuronal synapses.

cond-mat.stat-mech↗

arXiv2021

Arrival time for the fastest among $N$ switching stochastic particles

The first arrivals among $N$ Brownian particles is ubiquitous in the life sciences, as it often trigger cellular processes from the molecular level. We study here the case where stochastic particles, which represent molecules, proteins or molecules can switch between two states inside the non-negative real line. The switching process is modeled as a two-state Markov chain and particles can only escape in state 1. We estimate the fastest arrival time by solving asymptotically the Fokker-Planck equations for three different initial distributions: Dirac-delta, uniformly distributed and long-tail decay. The derived formulas reveal that the fastest particle avoid switching when the switching rates are much smaller than the diffusion time scale, but switches twice when the diffusion is state 2 is much faster than in state 1. The present results are compared to stochastic simulations revealing the range of validity of the derived formulas.

cond-mat.stat-mech↗

arXiv2020

Asymptotics for the fastest among n stochastics particles: role of an extended initial distribution and an additional drift component

We derive asymptotic formulas for the mean exit time $\bar{\tau}^{N}$ of the fastest among $N$ identical independently distributed Brownian particles to an absorbing boundary for various initial distributions (partially uniformly and exponentially distributed). Depending on the tail of the initial distribution, we report here a continuous algebraic decay law for $\bar{\tau}^{N}$, which differs from the classical Weibull or Gumbell results. We derive asymptotic formulas in dimension 1 and 2, for half-line and an interval that we compare with stochastic simulations. We also obtain formulas for an additive constant drift on the Brownian motion. Finally, we discuss some applications in cell biology where a molecular transduction pathway involves multiple steps and a long-tail initial distribution.

physics.data-an↗