Related papers: Large gap asymptotics for the generating function …
In this paper, we take the first step towards an extension of the nonlinear steepest descent method of Deift, Its and Zhou to the case of operator Riemann-Hilbert problems. In particular, we provide long range asymptotics for a Fredholm…
We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre ensembles, now studying the gap-probability generating functions. We show that the…
We demonstrate how the asymptotics for large $|z|$ of the generalised Bessel function \[{}_0\Psi_1(z)=\sum_{n=0}^\infty\frac{z^n}{\Gamma(an+b) n!},\] where $a>-1$ and $b$ is any number (real or complex), may be obtained by exploiting the…
We give the cumulative distribution function of $M_n$, the maximum of a sequence of $n$ observations from an ARMA(1, 1) process. Solutions are first given in terms of repeated integrals and then for the case, where the underlying random…
This paper is concerned with the characterizations of fixed points of the generating function of branching processes with countably infinitely many types. We assume each particle of type $i$ can only give offspring of type $j\geq i$, whose…
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
We study the probability of a real-valued stationary process to be positive on a large interval $[0,N]$. We show that if in some neighborhood of the origin the spectral measure of the process has density which is bounded away from zero and…
The singular values of a product of $M$ independent Ginibre matrices of size $N\times N$ form a determinantal point process. Near the soft edge, as both $M$ and $N$ go to infinity in such a way that $M/N\to \alpha$, $\alpha>0$, a scaling…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
In this work a method is presented to derive the generating functional in path integral form for a system with an arbitrary number of degrees of freedom and constrained by general conditions. The method is applied to the case of the…
We consider the gap probability for the Pearcey and Airy processes; we set up a Riemann--Hilbert approach (different from the standard one) whereby the asymptotic analysis for large gap/large time of the Pearcey process is shown to…
Given a diffeomorphism of the interval, consider the uniform norm of the derivative of its n-th iteration. We get a sequence of real numbers called the growth sequence. Its asymptotic behavior is an invariant which naturally appears both in…
A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…
Letting~$N=\left\{N(t), t\geq0\right\}$ be a standard Poisson process, Stroock~ \cite{Stroock-1981} constructed a family of continuous processes by $$\Theta_{\epsilon}(t)=\int_0^t\theta_{\epsilon}(r)dr, \ \ \ \ \ 0 \le t \le 1,$$ where…
Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a…
The short-time asymptotic behavior of the transition density function of the diffusion process generated by the general Grushin operator will be investigated, by using its explicit expression in terms of expectation. Further the dependence…
Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior…
We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show that if the underlying covariance function is regular and…
In this paper we prove a strong law of large numbers and its L^1-convergence counterpart for the process counted with a random characteristic in the context of self-similar fragmentation processes. This result extends a somewhat analogical…