Related papers: Random permutations without macroscopic cycles

Feller (1945) provided a coupling between the counts of cycles of various sizes in a uniform random permutation of $[n]$ and the spacings between successes in a sequence of $n$ independent Bernoulli trials with success probability $1/n$ at…

In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set $\{1,\dots,n\}$ under a particular class of multiplicative measures. Our method is based on generating functions…

Consider the dynamic environment governed by a Poissonian field of independent particles evolving as simple random walks on $\mathbb{Z}^d$. The random walk on random walks model refers to a particular stochastic process on $\mathbb{Z}^d$…

Berry Esseen type bounds to the normal, based on zero- and size-bias couplings, are derived using Stein's method. The zero biasing bounds are illustrated with an application to combinatorial central limit theorems where the random…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…

Since the appearance of H. Robbins article (1948), the central limit theorems for random sums have been studied for about 70 years. The central limit theorems for random sums of independent random variables play a very important role in…

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

Consider an ensemble of $N\times N$ non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded…

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 study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements $1,2,...,k$ are in distinct cycles of…

This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…

We study the number and distribution of the limit cycles of a planar vector field whose component functions are random polynomials. We prove a lower bound on the average number of limit cycles when the random polynomials are sampled from…

This paper focuses on the size-biased permutation of $n$ independent and identically distributed (i.i.d.) positive random variables. This is a finite dimensional analogue of the size-biased permutation of ranked jumps of a subordinator…

We consider two extremal problems for set systems without long Berge cycles. First we give Dirac-type minimum degree conditions that force long Berge cycles. Next we give an upper bound for the number of hyperedges in a hypergraph with…

We study fixed point biased involutions that avoid a pattern. For every pattern of length three we obtain limit theorems for the asymptotic distribution of the (appropriately centered and scaled) number of fixed points of a random fixed…

Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…

Given a Coxeter system of large type we prove a non--commutative central limit theorem: After normalisation with the square root of n the characteristic function of the set of the first n generators tends in distribution to Wigners…

We study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in…

We explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial…