Related papers: SPM Bulletin 31
We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness,…
In addition to announcements of several new papers, this issue contains a brief personal memorandum for Misha Matveev. The issue also announces the coming SPM meeting (June 2012).
The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.
Certain new inequalities for the sums of factorials are presented.
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…
A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…
These lecture notes are based on lectures given in 2019 Saint-Flour Probability School.
We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study…
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
A powerful statistical interpolating concept, which we call \emph{fully lifted} (fl), is introduced and presented while establishing a connection between bilinearly indexed random processes and their corresponding fully decoupled (linearly…
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of…
This is a quick survey on the characteristic varieties associated to rank one local systems on a smooth, irreducible, quasi-projective complex variety $M$. A key new result is Proposition 1.8, giving additional information on the…
The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are…
This review article is the second part of the project ``Selected Topics of Social Physics". The first part has been devoted to equilibrium systems. The present part considers nonequilibrium systems. The style of the paper combines the…
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial,…
This thesis studies advanced probabilistic models, including both their theoretical foundations and practical applications, for different semi-supervised learning (SSL) tasks. The proposed probabilistic methods are able to improve the…
In recent years, saliency ranking has emerged as a challenging task focusing on assessing the degree of saliency at instance-level. Being subjective, even humans struggle to identify the precise order of all salient instances. Previous…
We study structural aspects of randomized parameterized computation. We introduce a new class ${\sf W[P]}$-${\sf PFPT}$ as a natural parameterized analogue of ${\sf PP}$. Our definition uses the machine based characterization of the…
We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We…