Related papers: Permuton and local limits for the Luce model
We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the…
We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics…
The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…
We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in…
The goal of this paper is to analyse the asymptotic behavior of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens…
For a permuton $\mu$ let $H_n(\mu)$ denote the Shannon entropy of the sampling distribution of $\mu$ on $n$ points. We investigate the asymptotic growth of $H_n(\mu)$ for a wide class of permutons. We prove that if $\mu$ has a non-vanishing…
We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…
This paper gives a comprehensive treatment of local uniqueness, asymptotics and numerics for intrinsic means on the circle. It turns out that local uniqueness as well as rates of convergence are governed by the distribution near the…
We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show…
We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the L\"uck Approximation Theorem…
In statistics permutations typically arise in the context of rank plots for two-dimensional data. Such plots can also be interpreted as discrete copulas. In discrete mathematics, typically in the context of the description of large…
We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps $T_\alpha$ using the full parameter range $0<…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
We explore the probability that a permutation sampled from the symmetric group of order n uniformly at random has cycles of lengths not exceeding r. Asymptotic formulas valid in specified regions for the ratio n/r are obtained using the…