Related papers: Spatial random permutations with small cycle weigh…

We study the numerical range of an $n\times n$ cyclic shift matrix, which can be viewed as the adjacency matrix of a directed cycle with $n$ weighted arcs. In particular, we consider the change in the numerical range if the weights are…

We consider a random permutation drawn from the set of 132-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{\lambda(\sigma)/2}$ where…

This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…

Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The…

Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…

We discuss both simple and more subtle connections between the numbers of permutations and full cycles with some restrictions,in particular, between the numbers of permutations and full cycles with prescribed up-down structure.

This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in R^p as the number of points n -> infinity, while the dimension p is either fixed or growing with n. For both…

We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We…

In this article we consider the cycle structure of compositions of pairs of involutions in the symmetric group S_n chosen uniformly at random. These can be modeled as modified 2-regular graphs, giving rise to exponential generating…

We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive…

Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…

We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\pi \in \mathbb{S}_n$ is proportional to $q^{\textrm{inv}(\pi)}$ where $0<q\le 1$ and…

We consider a random permutation drawn from the set of permutations of length $n$ that avoid some given set of patterns of length 3. We show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after suitable…

In [Muhl2019], Peter M\"uhlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the percolation phase transition of the occupied edges. In this…

We consider a vertex reinforced random walk on the integer lattice with sub-linear reinforcement. Under some assumptions on the regular variation of the weight function, we characterize whether the walk gets stuck on a finite interval. When…

Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…

We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…

We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…

A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…

We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…