Related papers: On a method of introducing free-infinitely divisib…
We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…
We introduce a theory of probability in $\lambda$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the…
The standard method of transforming a continuous distribution on the line to the uniform distribution on the unit interval is the probability integral transform. Analogous transforms exist on compact Riemannian manifolds, in that, for each…
Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value -- namely, zero -- to cases that are impossible as well as to cases that are possible.…
We classify isomorphism-invariant random digraphs according to where randomness resides, namely, arcs, vertices, and vertices and arcs together which in turn yield arc random digraphs (ARD), vertex random digraphs (VRD) and vertex-arc…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…
We construct a random matrix model for the bijection \Psi between clas- sical and free infinitely divisible distributions: for every d\geq1, we associate in a quite natural way to each *-infinitely divisible distribution \mu a distribution…
We consider random holomorphic dynamical systems on the Riemann sphere whose choices of maps are related to Markov chains. Our motivation is to generalize the facts which hold in i.i.d. random holomorphic dynamical systems. In particular,…
Let a sequence of iid. random variables $\xi_1,...,\xi_n$ be given on a space $(X,\cal X)$ with distribution $\mu$ together with a nice class $\cal F$ of functions $f(x_1,...,x_k)$ of $k$ variables on the product space $(X^k,{\cal X}^k)$.…
We introduce multicritical Schur measures, which are probability laws on integer partitions which give rise to non-generic fluctuations at their edge. They are in the same universality classes as one-dimensional momentum-space models of…
We are concerned with three types of uncertainties: probabilistic, possibilitistic and interval. By using possibility and necessity measures as an Interval Valued Probability Measure (IVPM), we present IVPM's interval expected values whose…
We propose a parametric integral probability metric (IPM) to measure the discrepancy between two probability measures. The proposed IPM leverages a specific parametric family of discriminators, such as single-node neural networks with ReLU…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a probability measure to the space of discrete subgroups of…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint…
This extends a theorem of Davenport and Erd\"os on sequences of rational integers to sequences of integral ideals in arbitrary number fields $K$. More precisely, we introduce a logarithmic density for sets of integral ideals in $K$ and…
We discuss some natural maps from a unitary group U(n) to a smaller group U(n-m) (these maps are versions of the Livshic characteristic function). We calculate explicitly the direct images of the Haar measure under some maps. We evaluate…