Related papers: Gap probability for the hard edge Pearcey process
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
We consider the squared singular values of the product of $M$ standard complex Gaussian matrices. Since the squared singular values form a determinantal point process with a particular Meijer G-function kernel, the gap probabilities are…
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\beta$-ensembles. The conditioning is that…
We introduce a two parameter ($\alpha, \beta>-1$) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials $\{ P^{(\alpha, \beta)}_k \}_{k \geq 0}$. The family includes…
Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…
We discuss the experimental evidence supporting the concept of universality of the rapidity gap probability in soft and hard diffraction, relate the gap probability to hadronic parton densities, and present a phenomenological model of…
We prove sharp two-sided estimates on the tail probability of the first hitting time of bounded interval as well as its asymptotic behaviour for general non-symmetric processes which satisfy an integral condition \[ \int_0^{\infty}…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
We construct random point processes in the complex plane that are asymptotically close to a given doubling measure. The processes we construct are the zero sets of random entire functions that are constructed through generalised Fock…
This letter describes a direct method for computing the spatially averaged outage probability of a network with interferers located according to a point process and signals subject to fading. Unlike most common approaches, it does not…
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…
Our interest is in the cumulative probabilities Pr(L(t) \le l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions and reversed random fixed point free…
We adopt Gaussian Processes (GPs) as latent functions for probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function. We couple the latent…
When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based…
We consider the Pickands process {equation*} P_{n}(s)=\log (1/s)^{-1}\log \frac{X_{n-k+1,n}-X_{n-[k/s]+1,n}}{% X_{n-[k/s]+1,n}-X_{n-[k/s^{2}]+1,n}}, {equation*} {equation*} (\frac{k}{n}\leq s^2 \leq 1), {equation*} which is a generalization…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently describe a broad class of random tilings models,…
In this paper, we answer a question posed by Kurt Johansson, to find a PDE for the joint distribution of the Airy Process. The latter is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian…
We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n^{-1+eps} for every eps>0. This partly answers a question of Dudek and Frieze [Random Structures Algorithms],…
We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials. This identity is used to evaluate a triple asymptotic of some discrete…