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We study the probability distribution function (PDF) of the order parameter of the three-dimensional $O(N)$ model at criticality using the functional renormalisation group. For this purpose, we generalize the method introduced in [Balog et…
We use interface-resolved simulations to study finite-size effects in turbulent channel flow of neutrally-buoyant spheres. Two cases with particle sizes differing by a factor of 2, at the same solid volume fraction of 20% and bulk Reynolds…
Motivated by a recent random pipe dream model, we study a family of probability distributions on \(S_n\) arising from Bott--Samelson varieties over finite fields. More precisely, for a word \(R\), we consider the Bott--Samelson map…
We consider the $1d$ one-component plasma (OCP) in thermal equilibrium, consisting of $N$ equally charged particles on a line, with pairwise Coulomb repulsion and confined by an external harmonic potential. We study two observables: (i) the…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return…
Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically…
We study the role of renormalon cancellation schemes and perturbative scale choices in extractions of the strong coupling constant $\alpha_s(m_Z)$ and the leading non-perturbative shift parameter $\Omega_1$ from resummed predictions of the…
We present a rigorous description of the general problem of aperture photometry in high energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We compute the full posterior probability…
We study the scaling properties of latent diffusion models (LDMs) with an emphasis on their sampling efficiency. While improved network architecture and inference algorithms have shown to effectively boost sampling efficiency of diffusion…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
In this paper, we derive the joint asymptotic distributions of functions of quantile estimators (the non-parametric sample quantile and the parametric location-scale quantile estimator) with functions of measure of dispersion estimators…
A family of non-equilibrium statistical operators (NSO) is introduced which differ by the system lifetime distribution over which the quasi-equilibrium (relevant) distribution is averaged. This changes the form of the source in the…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…
We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the…
Count data are ubiquitous in ecology and the Poisson generalized linear model (GLM) is commonly used to model the association between counts and explanatory variables of interest. When fitting this model to the data, one typically proceeds…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
In the context of A. Eskin and A. Okounkov's approach to the calculation of the volumes of the different strata of the moduli space of quadratic differentials, two objects have a prominent role. Namely, the characters of near-involutions…
The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the ``small data'' limit where the number N of points in the training set is small. Many extensions have since been proposed,…