Related papers: A generalization of carries process and Eulerian n…
We study the ensemble-averaged conductance as a function of applied magnetic field for ballistic electron transport across few-channel microstructures constructed in the shape of classically chaotic billiards. We analyse the results of…
We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen…
We provide mathematicaly rigorous justification of using term "probability" in connection to the so called non-signalling theories,known also as Popescu's and Rohrlich's box worlds. No only do we prove correctness of these models (in the…
Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…
This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the…
We study the classical occupancy problem from the viewpoint of its embedding Markov chain. We derive new expressions for the probability mass function and (complementary) distribution function in generalized form. Furthermore, we derive a…
We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
In this paper, I will explain in as simple and intuitive physical terms as possible what generalized parton distributions are, what new information about the structure of hadrons they convey and therefore what picture of the hadron will…
Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with…
In this work, we extend the idea of Quantum Markov chains [S. Gudder. Quantum Markov chains. J. Math. Phys., 49(7), 2008] in order to propose Quantum Hidden Markov Models (QHMMs). For that, we use the notions of Transition Operation…
A universal scaling function, describing the crossover between the Mott and the Efros-Shklovskii hopping regimes, is derived, using the percolation picture of transport in strongly localized systems. This function is agrees very well with…
Recently, the second author studied an Eulerian statistic (called cover) in the context of convex polytopes, and proved an equal joint distribution of (cover,des) with (des,exc). In this paper, we present several direct bijective proofs…
We define a generalization of the Eulerian polynomials and the Eulerian numbers by considering a descent statistic on segmented permutations coming from the study of 2-species exclusion processes and a change of basis in a Hopf algebra. We…
Dynamical system properties give rise to effects in Statistical Mechanics. Topological index changes can be the basis for phase transitions. The Euler characteristic is a versatile topological invariant that can be evaluated for model…
We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' $q$-parametrized entropy. We discuss the dependence of the spacing distribution on $q$ using a non-extensive generalization of…
We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We…