Related papers: Daniel Litt's Probability Puzzle
In this paper we present three simple applications of probability and highlight and discuss their paradoxical flavour.
New cases of the multiplicity conjecture are considered.
We consider a special case of the generalized P\'{o}lya's urn model introduced by Benaim et al (2013). Given a finite connected graph $G$, place a bin at each vertex. Two bins are called a pair if they share an edge of $G$. At discrete…
Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the…
Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability…
Quantum probability theory and complex analysis for children.
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…
This article deals with some stochastic population protocols, motivated by theoretical aspects of distributed computing. We modelize the problem by a large urn of black and white balls from which at every time unit a fixed number of balls…
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…
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
Pilz's conjecture states that for any finite set $A=\{a_1,a_2,\dots,a_k\}$ of positive integers and positive integer $n$ in the union of the sets $\{a_1,2a_1,\dots,na_1\},\dots, \{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least…
This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…
In this paper three unrelated problems will be discussed. What connects them is the rich methodology of classical probability theory. In the first two problems we have a complete answer to the problems raised; in the third case, what we…
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…
Consider a P\'olya urn where a drawn ball of colour $i$ is replaced together with a fixed number $m_i$ of balls of the same colour. We give a simple proof that if, for example, there are two colours and the urn starts with more balls of…
Several results about the union-closed sets conjecture are presented.
In this article the propagation of pointlike event probabilities in space is considered. Double-Slit experiment is described in detail. New interpretation of Quantum Theory is formulated.
This paper presents duality between probability distributions and utility functions.