Related papers: Enumerative Theory for the Tsetlin Library
We consider a family of distributions on which natural tail orders can be constructed upon a representation of a distribution by a (single) hyper-real number. Past research revealed that the ordering can herein strongly depend on the…
Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider…
This paper is my contribution to the planned publication Recent Perspectives in Random Matrix Theory (Cambridge University Press). Addressed is the problem of computing spacing distributions in the bulk for the three symmetry classes…
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…
The Libra Toolkit is a collection of algorithms for learning and inference with discrete probabilistic models, including Bayesian networks, Markov networks, dependency networks, and sum-product networks. Compared to other toolkits, Libra…
We study the arithmetic circuit complexity of threshold secret sharing schemes by characterizing the graph-theoretic properties of arithmetic circuits that compute the shares. Using information inequalities, we prove that any unrestricted…
The central topic is this question: is a given $k$-\'etale algebra $\prod_lE_l/k$ the specialization of a given $k$-cover $f:X\rightarrow B$ at some point $t_0\in B(k)$? Our main tool is a {\it twisting lemma} that reduces the problem to…
In this paper we study the problem of the Malicious Maitre d', as described in Peter Winkler's book Mathematical Puzzles: A Connoisseur's Collection. This problem, attributed to computer scientist Rob Pike, involves seating diners around a…
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal…
We study a fair division problem with indivisible items, namely the computation of maximin share allocations. Given a set of $n$ players, the maximin share of a single player is the best she can guarantee to herself, if she would partition…
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…
Let $A$ be a real skew-symmetric Gaussian random matrix whose upper triangular elements are independently distributed according to the standard normal distribution. We provide the distribution of the largest singular value $\sigma_1$ of…
The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear…
Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get…
Markov logic uses weighted formulas to compactly encode a probability distribution over possible worlds. Despite the use of logical formulas, Markov logic networks (MLNs) can be difficult to interpret, due to the often counter-intuitive…
We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional…
In this paper, we develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new…
We consider families of exponential sums indexed by a subgroup of invertible classes modulo some prime power $q$. For fixed $d$, we restrict to moduli $q$ so that there is a unique subgroup of invertible classes modulo $q$ of order $d$. We…
Kingman's House-of-Cards model is a simple and celebrated model to describe the evolution of population under the competition of selection and mutation. Letting mutation probabilities vary on generations makes the model more realistic and…