Related papers: Modular Transformations, Order-Chaos Transitions a…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
The AMAS group at the Paul Scherrer Institute developed an object oriented library for high performance simulation of high intensity ion beam transport with space charge. Such particle-in-cell (PIC) simulations require a method to generate…
Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental…
Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
The pseudo-random number generators (PRNGs), sampling algorithms, and algorithms for generating random integers in some common statistical packages and programming languages are unnecessarily inaccurate, by an amount that may matter for…
Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend…
In this article, we study a non-uniform distribution on permutations biased by their number of records that we call \emph{record-biased permutations}. We give several generative processes for record-biased permutations, explaining also how…
An algorithm is presented which, with optimal efficiency, solves the problem of uniform random generation of distribution functions for an n-valued random variable.
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
We provide an efficient algorithm to generate random samples from the bounded kth order statistic in a sample of independent, but not necessarily identically distributed, random variables. The bounds can be upper or lower bounds and need…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
For one-dimensional random Schr\"odinger operators, the integrated density of states is known to be given in terms of the (averaged) rotation number of the Pr\"ufer phase dynamics. This paper develops a controlled perturbation theory for…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
This work addresses one-shot set and graph generation, and, more specifically, the parametrization of probabilistic decoders that map a vector-shaped prior to a distribution over sets or graphs. Sets and graphs are most commonly generated…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
In this paper we construct a pseudorandom multisequence $(x_{n_1,...,n_r})$ based on $k$th-order linear recurrences modulo $p$, such that the discrepancy of the $s$-dimensional multisequence $(x_{n_1+i_1,...,n_r+i_r})_{1 \leq i_j \leq s_j,…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…