Related papers: Walking into an absolute sum

Let $\Gamma$ be a countable group acting on a geodesic Gromov-hyperbolic metric space $X$ and $\mu$ a probability measure on $\Gamma$ whose support generates a non-elementary subsemigroup. Under the assumption that $\mu$ has a finite…

A combinatorial interpretation is provided for the moments of characteristic polynomials of random unitary matrices. This leads to a rather unexpected consequence of the Keating and Snaith conjecture: the moments of $\mid\xi(1/2+it)\mid$…

A random walk starts from the origin of a d-dimensional lattice. The occupation number n(x,t) equals unity if after t steps site x has been visited by the walk, and zero otherwise. We study translationally invariant sums M(t) of observables…

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

We study random walks on the integers mod $G_n$ that are determined by an integer sequence $\{ G_n \}_{n \geq 1}$ generated by a linear recurrence relation. Fourier analysis provides explicit formulas to compute the eigenvalues of the…

We study limit distributions for random variables defined in terms of coefficients of a power series which is determined by a certain linear functional equation. Our technique combines the method of moments with the kernel method of…

We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…

In a recent paper the authors studied the denominators of polynomials that represent power sums by Bernoulli's formula. Here we extend our results to power sums of arithmetic progressions. In particular, we obtain a simple explicit…

Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the…

Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…

One source of beauty in mathematics is totally unexpected connections between two fundamentally different objects. For instance, is it not surprising that the time period of a real simple pendulum is linked with a function arising out of…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

In this note, we compute the probability that a two-dimensional symmetric random walk visits more vertices than expected, for deviations on scales between the mean behavior and linear growth.

In this paper we prove some combinatorial identities which can be considered as generalizations and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach…

We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…

We present a definition for the sum of a sequence of combinatorial games. This sum coincides with the classical sum in the case of a converging sequence of real numbers and with the infinitary natural sum in the case of a sequence of…

We study some properties of the local time of the asymmetric Bernoulli walk on the line. These properties are very similar to the corresponding ones of the simple symmetric random walks in higher ($d\geq3$) dimension, which we established…

We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…

Denoting by $P_N(A,\theta)=\det(I-Ae^{-i\theta})$ the characteristic polynomial on the unit circle in the complex plane of an $N\times N$ random unitary matrix $A$, we calculate the $k$th moment, defined with respect to an average over…

We consider a simple dice game, which leads to an intriguing study of multinomial walks, with surprising and seemingly paradoxical properties. The winning and losing probabilities of a general version of the game are investigated via…