We study the length of cycles in the model of spatial random permutations in Euclidean
space. In this model, for given length L, density ρ ρ, dimension d and jump density φ φ, one …

Since the seminal work of Keating and Snaith, the characteristic polynomial of a random
Haar-distributed unitary matrix has seen several of its functional studied or turned into a …

We consider uniform random permutations of length n conditioned to have no cycle longer
than nβ with 0< β< 1, in the limit of large n. Since in unconstrained uniform random …

We consider random permutations on S_n with logarithmic growing cycles weights and
study the asymptotic behavior as the length n tends to infinity. We show that the cycle count …

The order O_n(σ) of a permutation σ of n objects is the smallest integer k≧1 such that the k-
th iterate of σ gives the identity. A remarkable result about the order of a uniformly chosen …

We explicitly compute limit shapes for several grand canonical Gibbs ensembles of
partitions of integers. These ensembles appear in models of aggregation and are also …

Random integers, sampled uniformly from [1, x], share similarities with random permutations,
sampled uniformly from S n. These similarities include the Erdős–Kac theorem on the …

We study the model of random permutations of n objects with polynomially growing cycle
weights, which was recently considered by Ercolani and Ueltschi, among others. Using …

This study extends a prior investigation of limit shapes for grand canonical Gibbs ensembles
of partitions of integers, which was based on analysis of sums of geometric random …

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 …