Related papers: Gap probabilities in the bulk of the Airy process
We study $n$ non-intersecting Brownian motions corresponding to initial configurations which have a vanishing density in the large $n$ limit at an interior point of the support. It is understood that the point of vanishing can propagate up…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In…
We consider the generating function of the sine point process on $m$ consecutive intervals. It can be written as a Fredholm determinant with discontinuities, or equivalently as the convergent series \begin{equation*} \sum_{k_{1},...,k_{m}…
This article presents a limit theorem for the gaps $\widehat{G}_{i:n}:= X_{n-i+1:n} - X_{n-i:n}$ between order statistics $X_{1:n} \le \cdots \le X_{n:n}$ of a sample of size $n$ from a random discrete distribution on the positive integers…
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…
We consider the point process of zeroes of certain Gaussian analytic functions and find the asymptotics for the probability that there are more than m points of the process in a fixed disk of radius r, as m-->infinity. For the Planar…
In this paper we investigate the statistics of large waiting times (with respect to the total waiting time) for Bernoulli processes. We determine the corresponding rate functions explicitly and prove a large deviations asymptotic. By this…
Let $A(p,n,k)$ be the number of $p$-tuples of commuting permutations of $n$ elements whose permutation action results in exactly $k$ orbits or connected components. We formulate the conjecture that, for every fixed $p$ and $n$, the…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
Let $\{X_i(t):\, t\in S\subset \R^d \}_{i=1,2,\ldots,n}$ be independent copies of a stationary centered Gaussian field with almost surely smooth sample paths. In this paper, we are interested in the conjunction probability defined as $\PP…
A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\'evy process with non-zero L\'evy measure. In this paper we study the asymptotic behavior of the local time process,…
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with…
We obtain the asymptotic behavior of hole probability for random holomorphic sections on a compact Riemann surface with respect to the hole size.
We study the asymptotics of the survival probability for the critical and decomposable branching processes in random environment and prove Yaglom type limit theorems for these processes. It is shown that such processes possess some…
The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed to show that the averaged coefficients may become…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…