Related papers: Geometric juggling with q-analogues

This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical…

We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…

A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes…

This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solution of the backward Kolmogorov equation, and (iii) as a…

This paper investigates the distribution of rational and algebraic points of bounded weighted height in weighted projective spaces over number fields. For a weighted projective space with weights q over a number field k of degree m, we…

We use numerical simulations and semi-analytical methods to investigate the stability and the interactions of nontopological stationary qball solutions. In the context of a simple model we map the parameter sectors of stability for a single…

We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…

In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random…

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming…

We study the canonical energy-momentum tensor of the spherically symmetric $U(1)$ gauged Q-ball configurations in the two-component Fridberg-Lee-Sirlin-Maxwell model, and in the one-component scalar model with a sixtic potential. We…

We analyze independent policy-gradient (PG) learning in $N$-player linear-quadratic (LQ) stochastic differential games. Each player employs a distributed policy that depends only on its own state and updates the policy independently using…

We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…

We characterise the permutations pi such that the elements in the closed lower Bruhat interval [id,pi] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the…

The cyclic sieving phenomenon provides a link between a polynomial analogue of Gauss congruence known as $q$-Gauss congruence, and a combinatorial analogue of Gauss congruence based on sequences of cyclic group actions. We strengthen this…

We apply to the $n\times n$ chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I showed that the number of ways to place $q$ identical…

This paper provides evidence that stock returns, after truncation, might be modeled by a special type of continuous mixtures or normals, so-called $q$-Gaussians. Negative binomial distributions might model the counts for extreme returns. A…

We study the nearest neighbors one dimensional uniform q-model of force fluctuations in bead packs [Coppersmith et al (1996)], a stochastic model to simulate the stress of granular media in two dimensional silos. The vertical coordinate…

We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…

We investigate integrable fermionic models within the scheme of the graded Quantum Inverse Scattering Method, and prove that any symmetry imposed on the solution of the Yang-Baxter Equation reflects on the constants of motion of the model;…

We show that a uniform quadrangulation, its largest 2-connected block, and its largest simple block jointly converge to the same Brownian map in distribution for the Gromov-Hausdorff-Prokhorov topology. We start by deriving a local limit…