Related papers: Scaling limits for the Lego discrepancy
We consider a three dimensional spatial network, where $N$ nodes are randomly distributed within a cube $L\times L\times L$. Each two nodes are connected if their mutual distance does not excess a given cutoff $a$. We analyse numerically…
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…
In this paper, we study the maximum likelihood estimation of the parameters of the multivariate and matrix variate symmetric Laplace distributions through group actions. The multivariate and matrix variate symmetric Laplace distributions…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
Wilf posed the following problem: determine asymptotically as $n\to\infty$ the probability that a randomly chosen part size in a randomly chosen composition of n has multiplicity m. One solution of this problem was given by Hitczenko and…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Maximum likelihood estimates (MLEs) are asymptotically normally distributed, and this property is used in meta-analyses to test the heterogeneity of estimates, either for a single cluster or for several sub-groups. More recently, MLEs for…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
A primary difficulty with unsupervised discovery of structure in large data sets is a lack of quantitative evaluation criteria. In this work, we propose and investigate several metrics for evaluating and comparing generative models of…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…