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The generalized Hastings-McLeod solutions to the inhomogeneous Painlev\'{e}-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths,…
We introduce a theory of probability in $\lambda$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the…
A meaningful probability distribution for measurements of a quantum stress tensor operator can only be obtained if the operator is averaged in time or in spacetime. This averaging can be regarded as a description of the measurement process.…
In this paper, we establish general scaling limits for nearly unstable Hawkes processes in a mean-field regime by extending the method introduced by Jaisson and Rosenbaum. Under a mild asymptotic criticality condition on the self-exciting…
The Hawkes process is a counting process that has self- and mutually-exciting features with many applications in various fields. In recent years, there have been many interests in the mean-field results of the Hawkes process and its…
The jump processes W(t) on [0,\infty[ with transitions w -> alpha w at rate b*w^beta (0 =< alpha =< 1, b>0, beta>0) are considered. Their moments are shown to decay not faster than algebraically for t -> \infty, and an equilibrium…
We study a class of integral functionals known as nonlocal perimeters, which, intuitively, express a weighted interaction between a set and its complement. The weight is provided by a positive kernel K, which might be singular. In the first…
Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the…
We consider the moderate deviations behaviors for two (co-) volatility estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The results are obtained by using a new result about the moderate deviations principle for…
The RG functions of the 2D $n$-vector $\phi^4$ model are calculated in the five-loop approximation. Perturbative series for the $\beta$ function and critical exponents are resummed by the Pade-Borel and Pade-Borel-Leroy techniques,…
Motivated by the study of the summatory $k$-free indicator and totient functions in the classical setting, we investigate their function field analogues. First, we derive an expression for the error terms of the summatory functions in terms…
Strong asymptotics of polynomials orthogonal on the unit circle with respect to a weight of the form $$ W(z) = w(z) \prod_{k=1}^m |z-a_k|^{2\beta_k}, \quad |z|=1, \quad |a_k|=1, \quad \beta_k>-1/2, \quad k=1, ..., m, $$ where $w(z)>0$ for…
The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman's Poisson-Dirichlet distribution. The two parameter Dirichlet…
For a family of random-cluster models with cluster weights $q\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$. The method developed in this article can…
The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…
We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on $\mathbb{Z}$, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the…
Using the Bethe ansatz we obtain the determinant expression for the time dependent transition probabilities in the totally asymmetric exclusion process with parallel update on a ring. Developing a method of summation over the roots of Bethe…
We study some asymptotic properties of cylinder processes in the plane defined as union sets of dilated straight lines (appearing as mutually overlapping infinitely long strips) derived from a stationary independently marked point process…
Links between uniform Aztec diamonds and random matrices are numerous in the literature. In particular \cite{johansson2006eigenvalues,Forrester} established that, under correct rescaling, the probability density function of a certain…
The bead process introduced by Boutillier is a countable interlacing of the determinantal sine-kernel point processes. We construct the bead process for general sine beta processes as an infinite dimensional Markov chain whose transition…