Related papers: Knuth's big-chooser matchbox process: the case of …
The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. Finding the steady state probability…
Using an identity arising in the known Banach probability problem on matchboxes, we prove an unexpected congruence for odd prime $p:$ for $1\leq k\leq \frac{p-1}{2},\enskip \sum_{i=1}^{p-2k-1}2^{i-1}\binom{k-1+i}{k}\equiv 0\pmod p.$
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select…
A simple analytical solution is proposed for the stationary loss system of two parallel queues with finite capacity $K$, in which new customers join the shortest queue, or one of the two with equal probability if their lengths are equal.…
We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove that for a…
Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…
Several differential equations usually appearing in mathematical physics are solved through a power series expansion, which reduces in solving difference equations. In this paper a probability problem is presented whose solution follows a…
We analyze sumsets A+B = {a+b : a in A, b in B} where A,B are sets of integers, A is infinite, and B has positive upper Banach density. For each k, we show that A+B contains at least the expected density of k-term arithmetic progressions…
When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…
In this paper the random channels and their compositions in the space of quantum states are studied. For compositions of i.i.d. random unitary channels, the limit behaviour of probability distributions is described. The sufficient condition…
Conjectures have historically played an important role in the development of pure mathematics. We propose a systematic approach to finding abstract patterns in mathematical data, in order to generate conjectures about mathematical…
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical…
Let $M$ be an ordered matching of size $n$, that is, a partition of the set $[2n]$ into 2-element subsets. The sock number of $M$ is the maximum size of a sub-matching of $M$ in which all left-ends of the edges precede all the right-ends…
A decisionmaker faces $n$ alternatives, each of which represents a potential reward. After investing costly resources into investigating the alternatives, the decisionmaker may select one, or more generally a feasible subset, and obtain the…
We observe a multilinearity preserving property of conditional expectation for infinite dimensional independent increment processes defined on some abstract Banach space $B$. It is similar in nature to the polynomial preserving property…
In this paper we introduce and study renewal-reward processes in random environments where each renewal involves a reward taking values in a Banach space. We derive quenched large deviation principles and identify the associated rate…
The mixing set with a knapsack constraint arises as a substructure in mixed-integer programming reformulations of chance-constrained programs with stochastic right-hand-sides over a finite discrete distribution. Recently, Luedtke et al.…
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to…
Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as $X\oplus Y$, then one of the closed subspaces $X$ or $Y$ must be finite dimensional. It…
We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues…