Related papers: The two-sided infinite extension of the Mallows mo…
Is this paper we study penalisations of diffusions satisfying some technical conditions, generalizing a result obtained by Najnudel, Roynette and Yor. If one of these diffusions has probability distribution $\mathbb{P}$, then our result can…
Random binary search trees are obtained by recursively inserting the elements $\sigma(1),\sigma(2),\ldots,\sigma(n)$ of a uniformly random permutation $\sigma$ of $[n]=\{1,\dots,n\}$ into a binary search tree data structure. Devroye (1986)…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
We introduce and study a new random permutation model that generalizes the $k$-card minimum model defined by Travers and the Mallows model. We calculate the permuton limit of such a sequence of random permutations. As a corollary, we deduce…
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…
Motivated by the work of Liu, we study certain canonical quotients of $G_{\emptyset}^T(K)$ -- the Galois group of the maximal unramified extension of a global field $K$ that is split completely at a finite nonempty set of places in $T$ --…
The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a…
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar non-equilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained…
We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities…
We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by Wang. More precisely, the resulting quantum groups…
In this paper we study the distribution of the size of the value set for a random polynomial with degree at most $q-1$ over a finite field $\mathbb{F}_q$. We obtain the exact probability distribution and show that the number of missing…
In this paper, we consider the distribution of the continuous paths of Dirichlet character sums modulo prime $q$ on the complex plane. We also find a limiting distribution as $q \rightarrow \infty$ using Steinhaus random multiplicative…
For a positive number $q$ the Mallows measure on the symmetric group is the probability measure on $S_n$ such that $P_{n,q}(\pi)$ is proportional to $q$-to-the-power-$\mathrm{inv}(\pi)$ where $\mathrm{inv}(\pi)$ equals the number of…
Answering a question of Geoff Robinson, we compute the large n limiting proportion of i(n,q)/q^[n^2/2], where i(n,q) denotes the number of involutions in GL(n,q). We give similar results for the finite unitary, symplectic, and orthogonal…
In this paper, we are interested in sequences of q-tuple of N-by-N random matrices having a strong limiting distribution (i.e. given any non-commutative polynomial in the matrices and their conjugate transpose, its normalized trace and its…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
A $\widetilde{Q}-$representation of real numbers is introduced as a generalization of the $p-$adic and $Q-$representations. It is shown that the $\widetilde{Q}-$representation may be used as a convenient tool for the construction and study…
We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…
We treat a random number generation from an i.i.d. probability distribution of $P$ to that of $Q$. When $Q$ or $P$ is a uniform distribution, the problems have been well-known as the uniform random number generation and the resolvability…
We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used…