Related papers: Three classical probability problems: the Hungaria…
A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.
We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can…
We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
Classical logic (the logic of non-constructive mathematics) is stronger than intuitionistic logic (the logic of constructive mathematics). Despite this, there are copies of classical logic in intuitionistic logic. All copies usually found…
This paper studies the existence and uniqueness of a classical solution to a type of Robin boundary problems on the nonnegative orthant. We propose a new decomposition-homogenization method for the Robin boundary problem based on…
We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
This article, based on a talk, treats some elementary, but not completely simple examples from probability. They concern multiple birthday coincidences, throwing dice, the combinatorics of the German card game "Doppelkopf", and the…
In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way…
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability…
We consider three problems from the recent issues of the American Mathematical Monthly involving different versions of Catalan triangle. Our main results offer generalizations of these identities and demonstrate automated proofs with…
It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random…
We revisit two classical problems: the determination of the law of the underlying with respect to a risk-neutral measure on the basis of option prices, and the pricing of options with convex payoffs in terms of prices of call options with…
Inspired by classical puzzles in geometry that ask about probabilities of geometric phenomena, we give an explicit formula for the probability that a random triangle on a flat torus is homotopically trivial. Our main tool for this…
The Stochastic Eulerian Tour Problem was introduced in 2008 as a stochastic variant of the well-known Eulerian Tour Problem. In a follow-up paper the same authors investigated some heuristics for solving the Stochastic Eulerian Tour…
This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this…
We use three kinds of computations: simulation, numeric, and symbolic, to guide risk-averse gamblers in general, and offer particular advice on how to resolve the famous St. Petersburg paradox.