相关论文: Sato-Tate Distribution of $p$-adic hypergeometric …

Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric…

We prove several results on the distribution of values of $L$-functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we study families of symmetric power…

Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…

We study $p$-adic Hodge theory for families of Galois representations over pseudorigid spaces. Such spaces are non-archimedean analytic spaces which may be of mixed characteristic, and which arise naturally in the study of eigenvarieties at…

We prove that the radial part of the class one Whittaker function on a split semisimple Lie group can be obtained as an appropriate limit of the Heckman-Opdam hypergeometric function.

The incomplete beta function is an important special function in statistics. In modern theory of hypergeometric functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles. However, the incomplete beta…

We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest.…

The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…

Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that their values are traces of Frobenius on…

For a real reductive group G, the center $\mathfrak{z}(\mathcal{U}(\mathfrak{g}))$ of the universal enveloping algebra of the Lie algebra $\mathfrak{g}$ of G acts on the space of distributions on G. This action proved to be very useful (see…

We study the derived Hecke action at $p$ on the ordinary $p$-adic cohomology of arithmetic subgroups of semisimple groups $\mathrm G(\mathbb Q)$, i.e., we study the derived version of Hida's theory for ordinary Hecke algebras. This is the…

In this article we use a covariance function that arises from limit of fluctuations of the rescaled occupation time process of a branching particle system, to introduce a family of weighted long-range dependence Gaussian processes. In…

Given a compact real hyperbolic space we study the connection between certain phase space distributions, so called Patterson-Sullivan distributions, and dynamical zeta functions. These zeta functions generalize logarithmic derivatives of…

We extend Urban's construction of eigenvarieties for reductive groups $G$ such that $G(\mathbb{R})$ has discrete series to include characteristic $p$ points at the boundary of weight space. In order to perform this construction, we define a…

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for…

Using the Bethe-Salpeter (B-S) equations for heavy baryons Lambda_Q, Sigma_Q, Xi_Q and Omega_Q (Q=b or c), which were established in previous work, we calculate the heavy quark distribution functions in these baryons. The numerical results…

As shown by Epstein and Glaser, the operator valued distribution (OPVD) formalism permits to obtain a non-standard regularization scheme which leads to a divergences-free quantum field theory. We show, with the example of a scalar quantum…

On finite regular graphs, we construct Patterson-Sullivan distributions associated with eigenfunctions of the discrete Laplace operator via their boundary values on the phase space. These distributions are closely related to Wigner…

We discuss algorithms for arithmetic properties of hypergeometric functions. Most notably, we are able to compute the p-adic valuation of a hypergeometric function on any disk of radius smaller than the p-adic radius of convergence. This we…

Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…