Related papers: A functional limit theorem for nested Karlin's occ…
We consider the problem of deterministic load balancing of tokens in the discrete model. A set of $n$ processors is connected into a $d$-regular undirected network. In every time step, each processor exchanges some of its tokens with each…
It is shown that large deviation statistical quantities of the discrete time, finite state Markov process $P_{n+1}^{(j)}=\sum_{k=1}^NH_{jk}P_n^{(k)}$, where P_n^{(j)} is the probability for the j-state at the time step n and H_{jk} is the…
We consider the classic infinite occupancy scheme, where balls are thrown in boxes independently, with probability $p_j$ of hitting box $j$. Each time a box receives its first ball we speak of a record and, more generally, call an…
We consider a sequence $(\xi_n)_{n\ge1}$ of $i.i.d.$ random values living in the domain of attraction of an extreme value distribution. For such sequence, there exists $(a_n)$ and $(b_n)$, with $a_n>0$ and $b_n\in\ER$ for every $n\ge 1$,…
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the…
In the paper we consider the partial sum process $\sum_{k=1}^{[nt]}X_k^{(n)}$, where $\{X_k^{(n)}=\sum_{j=0}^{\infty} a_{j}^{(n)}\xi_{k-j}(b(n)), \ k\in \bz\},\ n\ge 1,$ is a series of linear processes with tapered filter…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…
The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process…
The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and…
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…
We present a transplantation theorem for Jacobi coefficients in weighted spaces. In fact, by using a discrete vector-valued local Calder\'{o}n-Zygmund theory, which has recently been furnished, we prove the boundedness of transplantation…
Conditional sampling is a fundamental task in Bayesian statistics and generative modeling. Consider the problem of sampling from the posterior distribution $P_{X|Y=y^*}$ for some observation $y^*$, where the likelihood $P_{Y|X}$ is known,…
For the partial sums $(S_n)$ of independent random variables we define a stochastic process $s_n(t):=(1/d_n)\sum_{k \le [nt]} ({S_k}/{k}-\mu)$ and prove that $$(1/{\log N})\sum_{n\le N}(1/n)\mathbf {I}\left\{s_n(t)\le x\right\} \to…
A hallmark of certain topology, including the Chern number, is the obstruction to constructing exponentially localized Wannier functions in the bulk bands. Conversely, other types of topology do not necessarily impose Wannier obstructions.…
It is shown by constructing Rohlins canonical measures that for a strictly stationary, d-dimensional vector-valued process X there exists another strictly stationary d-dimensional process U with uniform one-dimensional marginals and with…
We study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory (also referred to as Wentzel-Kramers-Brillouin (WKB) method in some contexts). We obtain a general…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
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…