相关论文: Furstenberg systems of certain sequences of superp…
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…
We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models; depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first…
We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
Exponential sums with monomials are highly related to many interesting problems in number theory and well studied by many literatures. In this paper, we consider the exponential sums with polynomials and prove a new upper bound. As an…
We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but…
In modern usage the Bernoulli numbers and Bernoulli polynomials follow Euler's approach and are defined using generating functions. We consider the functional equation $f(x)+x^k=f(x+1)$ and show that a solution can be derived from…
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
We use the exponential random graph models to understand the network structure and its generative process for the Japanese bipartite network of banks and firms. One of the well known and simple model of exponential random graph is the…
We study the sup-norm and mean-square-norm problems for Eisenstein series on certain arithmetic hyperbolic orbifolds, producing sharp exponents for the modular surface and Picard 3-fold. The methods involve bounds for Epstein zeta…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
From genomes and ecosystems to bureaucracies and cities, the growth of complex systems occurs by adding new types of functions and expanding existing ones. We present a simple generative model that generalizes the Yule-Simon process by…
It is observed that the conjugacy growth series of the infinite finitary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…
Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…
We study the problem of expanding the product of two Stanley symmetric functions $F_w\cdot F_u$ into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert…
Recent developments in the theory and application of the Hardy-Littlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of…
The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…