Related papers: The weighted hook length formula
We employ a one-variable extension of q-rook theory to give combinatorial proofs of some basic hypergeometric summations, including the q-Pfaff-Saalsch\"utz summation and a 4phi3 summation by Jain.
In the present paper, we give the exact formula for the average hitting time (HT, as an abbreviation) of random walks from one vertex to any other vertex on the some weighted Cayley graphs.
We consider the edge-reinforced random walk with multiple (but finitely many) walkers which influence the edge weights together. The walker which moves at a given time step is chosen uniformly at random, or according to a fixed order.…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
In this note we observe that a bijection related to Littelmann's root operators (for type $A_1$) transparently explains the well known enumeration by length of walks on $\N$ (left factors of Dyck paths), as well as some other enumerative…
We consider a class of strongly edge-reinforced random walks, where the corresponding reinforcement weight function is nondecreasing. It is known, from Limic and Tarr\`{e}s [Ann. Probab. (2007), to appear], that the attracting edge emerges…
We count the number of walks of length n on a k-node circular digraph that cover all k nodes in two ways. The first way illustrates the transfer-matrix method. The second involves counting various classes of height-restricted lattice paths.…
The aim of this paper is to analyze the weighted KyFan inequality proposed in [11]. A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an…
We introduce a proof system for Hajek's logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL, are sound and invertible with respect to any valuation of BL into a suitable…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
We consider the branching capacity of the range of a simple random walk on $\mathbb Z^d$, with $d \ge 5$, and show that it falls in the same universality class as the volume and the capacity of the range of simple random walks and branching…
We consider the simple random walk on Z^d evolving in a potential of independent and identically distributed random variables taking values in [0, + \infty]. We give optimal conditions for the existence of the quenched point-to-point…
We derive a combinatorial equilibrium for bounded juggling patterns with a random, $q$-geometric throw distribution. The dynamics are analyzed via rook placements on staircase Ferrers boards, which leads to a steady-state distribution…
Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…
Let $(\xi_k, \eta_k)_{k\geq 1}$be independent identically distributed random vectors with arbitrarily dependent positive components and $T_k:=\xi_1+\ldots+\xi_{k-1}+\eta_k$for $k\in\mathbb{N}$. We call the random sequence {T_k, k=1,2...} a…
We prove strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type. This gives another application of a previous trimming result only proven for interval maps. In case of Markov measures we…
We study an approach to obtaining the exact formal solution of the 2-species Lotka-Volterra equation based on combinatorics and generating functions. By employing a combination of Carleman linearization and Mori-Zwanzig reduction…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
Consider a nearest neighbor random walk on the two-dimensional integer lattice, where each vertex is initially labeled either `H' or `V', uniformly and independently. At each discrete time step, the walker resamples the label at its current…
We calculate the one-loop effective potential for Horava-Lifshitz-like QED with an arbitrary critical exponent within different approaches and discuss its gauge dependence.