Related papers: Analysis and Probability on Infinite-Dimensional S…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
These are lecture notes for a mini-course given at the St. Petersburg School in Probability and Statistical Physics in June 2012. Topics include integrable models of random growth, determinantal point processes, Schur processes and Markov…
We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…
We extend the well-known characterizations of convergence in the spaces $l_p$ ($1\le p<\infty$) of $p$-summable sequence and $c_0$ of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis…
These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…
Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…
The differential-geometric structure of the set of positive densities on a given measure space has raised the interest of many mathematicians after the discovery by C.R. Rao of the geometric meaning of the Fisher information. Most of the…
In this thesis I develop a variety of techniques to train, evaluate, and sample from intractable and high dimensional probabilistic models. Abstract exceeds arXiv space limitations -- see PDF.
We study coercive inequalities in Orlicz spaces associated to the probability measures on finite and infinite dimensional spaces which tails decay slower than the Gaussian ones. We provide necessary and sufficient criteria for such…
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…
We construct for each $0<p\le 1$ an infinite collection of subspaces of $\ell_p$ that extend the example from [J. Lindenstrauss, On a certain subspace of $\ell_{1}$, Bull. Acad. Polon. Sci. S\'er. Sci. Math. Astronom. Phys. 12 (1964),…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. We present quantitative estimates for the rate of the convergence of the finite section method on weighted $\ell…
We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…
In infinite dimensional Banach spaces there is no complete characterization of the L\'evy exponents of infinitely divisible probability measures. Here we propose \emph{a calculus on L\'evy exponents} that is derived from some random…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…