相关论文: Geometric Characterization of the Eyring-Kramers F…

The Eyring-Kramers law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. In the weak-noise limit, the transition time is to leading order exponential in the potential…

Kramers' law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. We review different approaches that have been followed to obtain a mathematically rigorous proof of this…

We consider a class of parabolic semi-linear stochastic partial differential equations driven by space-time white noise on a compact space interval. Our aim is to obtain precise asymptotics of the transition times between metastable states.…

We consider two-dimensional stochastic differential equations, describing the motion of a slowly and periodically forced overdamped particle in a double-well potential, subjected to weak additive noise. We give sharp asymptotics of…

Thermally activated phenomena in physics and chemistry, such as conformational changes in biomolecules, liquid film rupture, or ferromagnetic field reversal, are often associated with exponentially long transition times described by…

We prove an Eyring-Kramers law for the small eigenvalues and mean first-passage times of a metastable Markovian jump process which is invariant under a group of symmetries. Our results show that the usual Eyring-Kramers law for asymmetric…

In the small noise regime, the average transition time between metastable states of a reversible diffusion process is described at the logarithmic scale by Arrhenius' law. The Eyring-Kramers formula classically provides a subexponential…

We address the Kramers escape problem for Brownian particles in bistable substrates with deformable double-well shapes. The shape deformability is considered of three distinct forms: in one, the positions of the two degenerate minima can be…

Consider the underdamped Langevin process $(q(t),p(t))_{t\geq0}$ in $\R^d\times\R^d$. We derive the low-temperature asymptotic of its mean-transition time between basins of attraction for a double-well potential. This asymptotic is called…

We consider non-reversible random walks evolving on a potential field in a bounded domain of $\mathbb{R}^d$. We describe the complete metastable behavior of the random walk among the landscape of valleys, and we derive the Eyring-Kramers…

We study ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin/fat tailed distributions, the normalized/non-normalised invariant…

We prove a Kramers-type law for metastable transition times for a class of one-dimensional parabolic stochastic partial differential equations (SPDEs) with bistable potential. The expected transition time between local minima of the…

We study the dynamics of a stochastic heat equation with $\gamma\sin(\beta u)$ nonlinearity on one-dimensional torus. We show an Eyring--Kramers law for the jump rate between potential wells in the small-noise limit, and that the transition…

We study spectral Galerkin approximations of an Allen--Cahn equation over the two-dimensional torus perturbed by weak space-time white noise of strength $\sqrt{\varepsilon}$. We introduce a Wick renormalisation of the equation in order to…

Let $(X_t)_{t\ge 0}$ be the stochastic process solution to the overdamped Langevin dynamics $$dX_t=-\nabla f(X_t) \, dt +\sqrt h \, dB_t$$ and let $\Omega \subset \mathbb R^d $ be the basin of attraction of a local minimum of $f: \mathbb…

Given an energy potential on the Euclidian space, a piecewise deterministic Markov process is designed to sample the corresponding Gibbs measure. In dimension one an Eyring-Kramers formula is obtained for the exit time of the domain of a…

We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on…

In this work, we derive a new sharp asymptotic equivalent in the small temperature regime $h\to 0$ for the mean exit time from a bounded domain for the non-reversible process $dX\_t=b(X\_t)dt + \sqrt h \, dB\_t$ under a generic orthogonal…

We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…

Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these…