Related papers: Hitting times distribution and extreme value law f…
Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…
We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. We determine the…
We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for…
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…
Forecasting extreme precipitation is essential yet challenging due to its rarity and complexity. We develop a large deviation framework to estimate the return times of extreme precipitation events. We first find that the Landau…
A complete characterization of the possible joint distributions of the maximum and terminal value of uniformly integrable martingale has been known for some time, and the aim of this paper is to establish a similar characterization for…
It is shown that time reversibility of Hamiltonian microscopic dynamics and Gibbs canonical statistical ensemble of initial conditions for it together produce an exact virial expansion for probability distribution of path of molecular…
We study a model of interacting vortices in a type II superconductor. In the weak coupling limit, we constructed a mean-field theory which allows us to accurately calculate the vortex density distribution inside a confining potential. In…
We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…
We consider a particle performing a stochastic motion on a one-dimensional lattice with jump widths distributed according to a power-law with exponent $\mu + 1$. Assuming that the walker moves in the presence of a distribution $a(x)$ of…
In this paper we study a boundary value problem for the Ricci flow in the two dimensional ball endowed with a rotationally symmetric metric. We show short and long time existence results. We construct families of metrics for which the flow…
We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
The time it takes the fastest searcher out of $N\gg1$ searchers to find a target determines the timescale of many physical, chemical, and biological processes. This time is called an extreme first passage time (FPT) and is typically much…
In this paper we study extreme events for random walks on homogeneous spaces. We consider the following three cases. On the torus we study closest returns of a random walk to a fixed point in the space. For a random walk on the space of…
In this paper we propose a new concept to prioritize the importance of a link in a directed network graph based on an ideal flow distribution. An ideal flow is the infinite limit of relative aggregated count of random walk agents'…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
We consider invariant measures of maps on manifolds whose correlations decay at a sufficient rate and which satisfy a geometric contraction property. We then prove the that the limiting distribution of returns to geometric balls is…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…