Related papers: Large gap asymptotics for Airy kernel determinants…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of…
String equations related to 2D gravity seem to provide, quite naturally and systematically, integrable kernels, in the sense of Its-Izergin-Korepin and Slavnov. Some of these kernels (besides the "classical" examples of Airy and Pearcey)…
We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states…
We show, using either Fock space techniques or Macdonald difference operators, that certain symplectic and orthogonal analogues of Okounkov's Schur measure are determinantal with kernels given by explicit double contour integrals. We give…
We study $n\times n$ Hankel determinants constructed with moments of a Hermite weight with a Fisher-Hartwig singularity on the real line. We consider the case when the singularity is in the bulk and is both of root-type and jump-type. We…
A general method of finding functional determinants is presented that depends on the asymptotic behaviour of the resolvent. Its application to the case of a bounded trihedral corner for which the eigenvalues are known only implicitly is…
We consider fourth order ordinary differential operators with compactly supported coefficients on the half-line and on the line. The Fredholm determinant for this operator is an analytic function in the whole complex plane without zero. We…
We explain a discontinuous drop in the exponential growth rate for certain multivariate generating functions at a critical parameter value, in even dimensions d at least 4. This result depends on computations in the homology of 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…
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…
This paper is the first in a series of three. The main result, Theorem 1.11, gives an explicit description of the ergodic decomposition for infinite Pickrell measures on spaces of infinite complex matrices. The main construction is that of…
We consider a two-dimensional point process whose points are separated into two disjoint components by a hard wall, and study the multivariate moment generating function of the corresponding disk counting statistics. We investigate the…
Let $F$ be a non-discrete non-Archimedean local field. For any subset $S\subset F$ with finite Haar measure, there is a stationary determinantal point process on $F$ with correlation kernel $\widehat{\mathbb{1}}_S(x-y)$, where…
Linear second order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two…
The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
Motivated by some recent potential theoretic results on subordinate killed L\'evy processes in open subsets of the Euclidean space, we study processes in an open set $D\subset {\mathbb R}^d$ defined via Dirichlet forms with jump kernels of…