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We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of…
We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space,…
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…
Let $A \subset \mathbb{R}^d$, $d\ge 2$, be a compact convex set and let $\mu = \varrho_0 dx$ be a probability measure on $A$ equivalent to the restriction of Lebesgue measure. Let $\nu = \varrho_1 dx$ be a probability measure on $B_r :=…
Numerical simulations including magnetic fields have become important in many fields of astrophysics. Evolution of magnetic fields by the constrained transport algorithm preserves magnetic divergence to machine precision, and thus…
In this work, we present a theoretical and computational framework for constructing stochastic transport maps between probability distributions using diffusion processes. We begin by proving that the time-marginal distribution of the sum of…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random covering condition. Given a random contracting potential $\varphi$…
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
This work studies the quantitative stability of the quadratic optimal transport map between a fixed probability density $\rho$ and a probability measure $\mu$ on R^d , which we denote T$\mu$. Assuming that the source density $\rho$ is…
Given a surface $M$ and a Borel probability measure $\nu$ on the group of $C^2$-diffeomorphisms of $M$, we study $\nu$-stationary probability measures on $M$. Assuming the positivity of a certain entropy, the following dichotomy is proved:…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability…
We consider ultraweak variational formulations for (parametrized) linear first order transport equations in time and/or space. Computationally feasible pairs of optimally stable trial and test spaces are presented, starting with a suitable…
A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in [Avigad et al. 2010,…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…