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Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function $P(X,t)$ of packets of spreading random walkers, were observed in numerous situations…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…
Let $\pi_{0}$ and $\pi_{1}$ be two distributions on the Borel space $(\mathbb{R}^{d},\mathcal{B}(\mathbb{R}^{d}))$. Any measurable function $T:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d}$ such that $Y=T(X)\sim\pi_{1}$ if $X\sim\pi_{0}$ is…
Using the techniques developed in arxiv: 1203.3544 we compute the universal part of the equilibrium partition function characteristic of a theory with multiple abelian U(1) anomalies in arbitrary even spacetime dimensions. This contribution…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
We study sampling properties of the zero set of the Gaussian entire function on Fock spaces. Firstly, we relax Seip and Wallst\'en's density and separation conditions for sampling sets on Fock spaces to obtain weighted inequalities for sets…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
We study stationary solutions to the continuity equation for weakly compressible flows. These describe non-equilibrium steady states of weakly dissipative dynamical systems. Compressibility is a singular perturbation that changes the steady…
We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…
According to a general probabilistic principle, the natural divisors of friable integers (i.e.~free of large prime factors) should normally present a Gaussian distribution. We show that this indeed is the case with conditional density…