Related papers: The Elliptic Tail Kernel
The Katz-Sarnak philosophy states that statistics of zeros of $L$-function families near the central point as the conductors tend to infinity agree with those of eigenvalues of random matrix ensembles as the matrix size tends to infinity.…
We study the correlation functions for determinantal point processes defined by products of infinite minors of block Toeplitz matrices. The motivation for studying such processes comes from doubly periodically weighted tilings of planar…
In this work we introduce a family of transformations, named \textit{divergence transformations}, interpolating between any pair of probability density functions sharing the same support. We prove the remarkable property that the whole…
The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E…
Two-dimensional QCD with $N_c$ colors and $N_f$ flavors of massless fermions in the fundamental representation is expected to exhibit conformal behavior in the infrared governed by a $u(N_f)$ WZW model with level $N_c$. Using numerical…
We consider the q-Hahn TASEP which is a three-parameter family of discrete time interacting particle systems. The particles jump to the right independently according to a certain q-Binomial distribution with parallel updates. It is a…
In Part I (G.Olshanski, math.RT/9804086) and Part II (A.Borodin, math.RT/9804087) we developed an approach to certain probability distributions on the Thoma simplex. The latter has infinite dimension and is a kind of dual object for the…
The transformation behaviour of the vector valued theta function of a positive-definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation. We show that the invariants of this…
In this paper we study the cross section at leading order in $1/Q$ for polarized Drell-Yan scattering at measured lepton-pair transverse momentum $Q_T$. We find that for a hadron with spin $1/2$ the quark content at leading order is…
We study the integro-differential operators $L$ with kernels $K(y) = a(y) J(y)$, where $J(y)dy$ is a L\'evy measure on $\bR^d$ (i.e. $\int_{\bR^d}(1\wedge |y|^2)J(y)dy<\infty$) and $a(y)$ is an only measurable function with positive lower…
Several rotational invariant quantities for the lepton angular distributions in Drell-Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames.…
In the context of lattice walk enumeration in cones, we consider the number of walks in the quarter plane with fixed starting and ending points, prescribed step-set and given length. After renormalization, this number may be interpreted as…
Topological strings on Calabi--Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi--Yau threefolds given by a bundle over a two-sphere.…
I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main…
For a finite field $\mathbb{F}_q$ of characteristic $p\geq 5$ and $K=\mathbb{F}_q(t)$, we consider the family of elliptic curves $E_d$ over $K$ given by $y^2+xy - t^dy=x^3$ for all integers $d$ coprime to $q$. We provide an explicit…
We present a theoretical study of the azimuthal decorrelation $\delta\phi$ and transverse momentum imbalance $q_T$ in dijet production at the LHC, offering intriguing insights into the dynamics of quantum chromodynamics. We define the jet…
The simplest orientifolds of the WZW models are obtained by gauging a Z_2 symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted…
This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that…
We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal…
The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric properties of the lattice we give the…