Related papers: Continuum statistics of the Airy2 process

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…

In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed…

We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the…

We study the distribution of the supremum of the Airy process with $m$ wanderers minus a parabola, or equivalently the limit of the rescaled maximal height of a system of $N$ non-intersecting Brownian bridges as $N\to\infty$, where the…

We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…

We investigate the characteristic polynomials of the Gaussian $\beta$-ensemble for general $\beta>0$ through its transfer matrix recurrence. We show that the rescaled characteristic polynomial converges to a random entire function in a…

We show that the endpoint large deviation rate function for a continuous-time directed polymer agrees with the rate function of the underlying random walk near the origin in the whole weak disorder phase.

Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…

We prove that certain asymptotic moments exist for some random distance expanding dynamical systems and Markov chains in random dynamical environment, and compute them in terms of the derivatives at the $0$ of an appropriate pressure…

The asymptotic analytic expression for the two-time free energy distribution function in (1+1) random directed polymers is derived in the limit when the two times are close to each other

We consider the statistical mechanics of a random polymer with random walks and disorders in $\mathbb{Z}^d$. The walk collects random disorders along the way and gets nothing if it visits the same site twice. In the continuum and weak…

We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new…

A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…

We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…

In this manuscript we consider the set of Dyck paths equipped with the uniform measure, and we study the statistical properties of a deformation of the observable "area below the Dyck path" as the size $N$ of the path goes to infinity. The…

For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…

There is considerable current interest in the emergence of statistical correlations within a population of otherwise non-interacting Brownian particles subject to a common fluctuating environment or drive. Examples include global stochastic…

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their…

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…