Related papers: Factorizing random sets and type III Arveson syste…
Stationary Gaussian generalized random processes having slowly decreasing spectral densities give rise to product systems in the sense of William Arveson (basically, continuous tensor product systems of Hilbert spaces). A continuum of…
We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of…
We describe a construction for producing Keisler measures on bounded perfect PAC fields. As a corollary, we deduce that all groups definable in bounded perfect PAC fields, and even in unbounded perfect Frobenius fields, are definably…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
We develop a principled methodology to infer assortative communities in networks based on a nonparametric Bayesian formulation of the planted partition model. We show that this approach succeeds in finding statistically significant…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…
We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural definition in terms of Young tableaux, is a deformation of…
It was recently proven that, in contrast to their matrix analogues, the moments of a real Gaussian tensor of size N do not in general factorize over their connected components in the asymptotic large N limit. While the original proof of…
We construct random point processes in the complex plane that are asymptotically close to a given doubling measure. The processes we construct are the zero sets of random entire functions that are constructed through generalised Fock…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…
Thermodynamic irreversibility is a fundamental concept in statistical physics, yet its experimental measurement remains challenging, especially for complex systems. We introduce a novel random coarse-graining framework to identify…
The factorizable vectors of a complete Boolean algebra of type I factors, acting on a separable Hilbert space, are shown to be total, resolving a conjecture of Araki and Woods. En route, the spectral theory of noise-type Boolean algebras of…
Multivariate sample spaces may be incomplete Cartesian products, when certain combinations of the categories of the variables are not possible. Traditional log-linear models, which generalize independence and conditional independence, do…
We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures sets, that are non necessarily compact but generated by their extreme points. We show that the maximum of a quasi-convex lower…
We propose compactifications of the moduli space of Bridgeland stability conditions of a triangulated category. Our construction arises from a viewing a stability condition as a metric on the underlying category and is inspired by the…
We study several model-theoretic aspects of W$^*$-probability spaces, that is, $\sigma$-finite von Neumann algebras equipped with a faithful normal state. We first study the existentially closed W$^*$-spaces and prove several structural…
In the additive topological group $(\mathbb{R},+)$ of real numbers, we construct families of sets for which elements are not measurable in the Lebesgue sense. The constructed families have algebraic structures of being semigroups (i.e.,…
With every Eo-semigroup (acting on the algebra of of bounded operators on a separable infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most important results about Arveson systems is that every Arveson…