Related papers: Daniel Litt's Probability Puzzle

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…

Consider a number, finite or not, of urns each with fixed capacity $r$ and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain $r$ balls. When $r=1$, using analytic…

I explore the use of sets of probability measures as a representation of uncertainty.

The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability.…

This is a survey of old and new problems and results in additive number theory.

This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economically and in a uniform way, categories ofstructures dually…

We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.

We use probability urn models to discover some known and unknown series identities involving Fibonacci numbers.

We consider predictive inference using a class of temporally dependent Dirichlet processes driven by Fleming--Viot diffusions, which have a natural bearing in Bayesian nonparametrics and lend the resulting family of random probability…

In this paper we give a formula for the probability that $n$ random points chosen under the uniform distribution in a disk are in convex position. While close, the formula is recursive and is totally explicit only for the first values of…

This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.

We provide infinitely many solutions of a Dirichlet problem on balls.

Dan Reznik found, by computer experimentation, a number of conserved quantities associated with periodic billiard trajectories in ellipses. We prove some of his observations using a non-standard generating function for the billiard ball…

Here I discuss ideas that makes a synthesis of topology and probability theory. The idea is the following: given a set $X$, assign a number $p(A)\in [0,1]$ for any subset $A$ of $X$. We can interpret $p(A)$ as the probability of openness of…

Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures…

We present a conclusive answer to Bertrand's paradox, a long standing open issue in the basic physical interpretation of probability. The paradox deals with the existence of mutually inconsistent results when looking for the probability…

This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.

I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…

Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…