Related papers: Recent progress on conditional randomness

There is a lot of research on probabilistic transition systems. There are not many studies in probabilistic process models. The lack of investigation into the interactive aspect of probabilistic processes is mainly due to the difficulty…

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…

In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…

For each $n$, let $M_n$ be an $n\times n$ random matrix with independent $\pm 1$ entries. We show that ${\mathbb P}\{\mbox{$M_n$ is singular}\}=(1/2+o_n(1))^n$, which settles an old problem. Some generalizations are considered.

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

In the context of generalized measurement theory, the Gleason-Busch theorem assures the unique form of the associated probability function. Recently, in Flatt et al. Phys. Rev. A 96, 062125 (2017), the case of subsequent measurements has…

We describe recent advances in the study of random analogues of combinatorial theorems.

The sum of $n$ {non-independent} Bernoulli random variables could be modeled in several different ways. One of these is the Multiplicative Binomial Distribution (MBD), introduced by Altham (1978) and revised by Lovison (1998). In this work,…

A novel multinomial theorem for commutative idempotents is shown to lead to new results about the moments, central moments, factorial moments, and their generating functions for any random variable $X = \sum_{i} Y_i $ expressible as a sum…

We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.

In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…

I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.

The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval $[0,R]$ is almost surely an orthogonal polynomial ensemble. In this article, we show that if $R$ tends to…

We prove a new hypothesis on the conditional distribution of the sample mean of the fluctuations of an i.i.d. random potential in the Anderson model. The paper extends to uniform probability distribution some earlier work with Gaussian…

Let $M_n$ denote a random symmetric $n \times n$ matrix whose upper diagonal entries are independent and identically distributed Bernoulli random variables (which take values $1$ and $-1$ with probability $1/2$ each). It is widely…

The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…

In a celebrated work by Hoeffding [J. Amer. Statist. Assoc. 58 (1963) 13-30], several inequalities for tail probabilities of sums M_n=X_1+... +X_n of bounded independent random variables X_j were proved. These inequalities had a…

In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…