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A common approach to analyze count time series is to fit models based on random sum operators. As an alternative, this paper introduces time series models based on a random multiplication operator, which is simply the multiplication of a…
We consider nearest-neighbor random walks on free products of finitely many copies of the integers with amalgamation over nontrivial subgroups. When all the subgroups have index two, we find the Green function of the random walks in terms…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…
As more of topology's tools become popular in analyzing high dimensional data sets, the goal of understanding the underlying probabilistic properties of these tools becomes even more important. While much attention has been given to…
We show that Araki and Masuda's weighted non-commutative vector valued $L_p$-spaces [Araki \& Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)] correspond to an algebraic generalization of the sandwiched R\'enyi divergences with parameter…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
A meromorphic transform between complex manifolds is a surjective mutivalued map with an analytic graph. Let $F_n$ be a sequence of meromorphic transforms from a compact Kahler manifold X into compact Kahler manifolds X_n. We give…
In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$,…
We provide a probabilistic analysis of the banker algorithm when transition probabilities may depend on time and space. The transition probabilities evolve, as time goes by, along the trajectory of an ergodic Markovian environment, whereas…
We consider here a class of groupoids obtained via an equivalence relation (the subgroupoids of pair groupoids). We generalize to Haar Systems in these groupoids some results related to entropy and pressure which are well known in…
Our goal in this paper is to investigate four conjectures proposed by Daqing Wan about the stable behavior of a geometric $\mathbb{Z}_p$-tower of curves $X_{\infty}/X$. Let $h_n$ be the class number of the $n$-th layer in $X_{\infty}/X$. It…
Given a random walk a method is presented to produce a matrix of transition probabilities that is consistent with that random walk. The method is a kind of reverse application of the usual ergodicity and is tested by using a transition…
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…
We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier…
Consider a random walk $S_i= \xi_1+\ldots+\xi_i$, $i\in\mathbb N$, whose increments $\xi_1,\xi_2,\ldots$ are independent identically distributed random vectors in $\mathbb R^d$ such that $\xi_1$ has the same law as $-\xi_1$ and $\mathbb…
In this paper, we apply results of \cite{Va3} and use towers to transfer symmetry from $\mu^+$ down to $\mu$ in superstable abstract elementary classes without using extra set-theoretic assumptions or tameness. Theorem. Suppose…
In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…