Related papers: An ergodic theorem for partially exchangeable rand…
This paper is devoted to the study of a stochastic process obtained by random switching between a finite collection of vector fields. Such processes have recently been the focus of much attention in the case where the switching times are…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…
We study statistics on ordered set partitions whose generating functions are related to $p,q$-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of \stein…
This note attempts to understand graph limits as defined by Lovasz and Szegedy (2006)} in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of…
We present a new proof of an Ergodic theorem for Wide-Sense Stationary Random Processes added with a new canonical sampling theorem of mine for finite time duration signals in the frequency domain (periodograms) which is free from the…
A theory which describes the share price evolution at financial markets as a continuous-time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Let $F(N,m)$ denote a random forest on a set of $N$ vertices, chosen uniformly from all forests with $m$ edges. Let $F(N,p)$ denote the forest obtained by conditioning the Erdos-Renyi graph $G(N,p)$ to be acyclic. We describe scaling limits…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth $X_i$ and $X_j$ are redistributed by flipping a sequence of fair coins leading to a…
In this paper we study the small scale equidistribution property of random waves whose coefficients are determined by an unfair coin. That is the coefficients take value $+1$ with probability $p$ and $-1$ with probability $1-p$. Random…
Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
We study the long time evolution and stationary speed distribution of N point particles in 2D moving under the action of an external field E, and undergoing elastic collisions with either a fixed periodic array of convex scatterers, or with…
Pi Fractions are used to create deterministic uniformly distributed pseudorandom decision space sample points for a global search and optimization algorithm. These fractions appear to be uniformly distributed on [0,1] and can be used in any…
Let $G=(V,E)$ be a random electronic network with the boundary vertices which is obtained by assigning a resistance of each edge in a random graph in $\mathbb{G}(n,p)$ and the voltages on the boundary vertices. In this paper, we prove that…
A sequence of random variables is called \textit{exchangeable} if its joint distribution is invariant under permutations of indices. The original formulation of de Finetti's theorem roughly says that any exchangeable sequence of…
We create mechanically stable (MS) packings of bidisperse disks using an algorithm in which we successively grow or shrink soft repulsive disks followed by energy minimization until the overlaps are vanishingly small. We focus on small…
The coherent quantum dynamics of an electron in the quantum-dot ring structure under the resonant electromagnetic pulse is studied theoretically. A possibility of the selective electron transfer between any two dots is demonstrated. The…