Related papers: Leap generators for composition schemes

We study a random walk on the Lie algebra $\mathfrak{sl}_2(\mathbf{F}_p)$ where new elements are produced by randomly applying adjoint operators of two generators. Focusing on the generic case where the generators are selected at random, we…

This article introduces a new approach to principled and practical random variate generation with formal guarantees. The key idea is to first specify the desired probability distribution in terms of a finite-precision numerical program that…

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…

Multitudinous probabilistic and combinatorial objects are associated with generating functions satisfying a composition scheme $F(z)=G(H(z))$. The analysis becomes challenging when this scheme is critical (i.e., $G$ and $H$ are…

Random graphs with prescribed degree sequences have been widely used as a model of complex networks. Comparing an observed network to an ensemble of such graphs allows one to detect deviations from randomness in network properties. Here we…

We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are L\'evy flights, where the walkers…

Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname…

Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…

This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are…

Recent advances in generative modeling, namely Diffusion models, have revolutionized generative modeling, enabling high-quality image generation tailored to user needs. This paper proposes a framework for the generative design of structural…

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a…

A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…

We give an $m^{1+o(1)}\beta^{o(1)}$-time algorithm for generating a uniformly random spanning tree in an undirected, weighted graph with max-to-min weight ratio $\beta$. We also give an $m^{1+o(1)}\epsilon^{-o(1)}$-time algorithm for…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

We develop uniformly fast random variate generators for the Pearson IV distribution that can be used over the entire range of both shape parameters and highlight some applications in a Bayesian setting.

Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…

We present a novel Adaptive Distribution Generator that leverages a quantum walks-based approach to generate high precision and efficiency of target probability distributions. Our method integrates variational quantum circuits with…

A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…

We study a new class of time inhomogeneous P\'olya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma…