Related papers: Haldane-Wu statistics and Rogers dilogarithm
A generalization of the Lambert W function called the logarithmic Lambert function is found to be a solution to the thermostatics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor…
Let $(\mu_{\alpha})$ be a net of Radon sub-probability measures on the real line, and $(t_{\alpha})$ be a net in $]0,+\infty[$ converging to 0. Assuming that the generalized log-moment generating function $L(\lambda)$ exists for all…
Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…
Counting ad infinitum is the holographic observable to a statistical dynamics with finite states under independent repeated sampling. Entropy provides the infinitesimal probability for an observed frequency $\hat{\boldsymbol{\nu}}$ w.r.t. a…
The thermodynamics of the dissipative two-state system is calculated exactly for all temperatures and level asymmetries for the case of Ohmic dissipation. We exploit the equivalence of the two-state system to the anisotropic Kondo model and…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under non-equilibrium conditions, we show that the first derivative of the cumulant…
W-operators are differential operators on the polynomial ring. Mironov, Morosov and Natanzon construct the generalized Hurwitz numbers. They use the W-operator to prove a formula for the generating function of the generalized Hurwitz…
We study a discrete analogue of the classical multivariate Gaussian distribution. It is supported on the integer lattice and is parametrized by the Riemann theta function. Over the reals, the discrete Gaussian is characterized by the…
The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general {\it{less}} than the number of independent primary…
We propose an extension of the numerical approach for integrable Richardson-Gaudin models based on a new set of eigenvalue-based variables. Starting solely from the Gaudin algebra, the approach is generalized towards the full class of XXZ…
In this paper we are concerned with the study of additive ergodic averages in multiplicative systems and the investigation of the "pretentious" dynamical behaviour of these systems. We prove a mean ergodic theorem (Theorem A) that…
The discussion of Fractional dimensional Hilbert spaces in the context of Haldane exclusion statistics is extended from the case \cite{IG} of $g=1/p$ for the statistical parameter to the case of rational $g=q/p$ with $q,p$-coprime positive…
We consider the Laguerre partition function, and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was recently proven that correlators have a…
It has been argued in [EPL {\bf 90} (2010) 50004], entitled {\it Essential discreteness in generalized thermostatistics with non-logarithmic entropy}, that "continuous Hamiltonian systems with long-range interactions and the so-called…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…
We study the operator product expansions in the chiral algebra $\mathcal{W}_{\infty}$, first using the associativity conditions in the basis of primary generating fields and second using a different basis coming from the free field…
A model to explain the statistics of the velocity gradients in the dissipation range of a turbulent flow is presented. The experimentally observed non-gaussian statistics is theoretically predicted by means of a thermodynamical analogy…
The XXX Heisenberg model is studied at finite temperature. The free energy is derived without recourse to Thermal Bethe Ansatz method and Quantum Transfer Matrix method. The result perfectly agrees with the free energy derived by Thermal…
We first reobtain in a simpler way the Haldane fractional statistics at thermal equilibrium using an interpolation argument. We then show that the mean occupation number for fractional statistics is invariant to a group of duality…