Related papers: Traffic Distributions and Independence II: Univers…
Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail,…
We investigate metric conditions that allow to prove existence and uniqueness of a map solving the Monge problem between two marginals in a metric (measure) space, proving two main results. Firstly, we introduce a nonsmooth version of the…
Transportation maps between probability measures are critical objects in numerous areas of mathematics and applications such as PDE, fluid mechanics, geometry, machine learning, computer science, and economics. Given a pair of source and…
The analysis of GPS trajectories is a well-studied problem in Urban Computing and has been used to track people. Analyzing people mobility and identifying the transportation mode used by them is essential for cities that want to reduce…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster…
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…
A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of products of the matrices). We introduce the…
This work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the…
Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…
Let $a_{1},...,a_{n}, b_{1},...,b_{n}$ be random variables in some (non-commutative) probability space, such that $\{a_{1}, ..., a_{n} \}$ is free from $\{b_{1}, ..., b_{n} \}$. We show how the joint distribution of the $n$-tuple $(a_{1}…
In this note, we show that the limiting spectral distribution of symmetric random matrices with stationary entries is absolutely continuous under some sufficient conditions. This result is applied to obtain sufficient conditions on a…
The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity…
In this paper, we will construct the graph free product of noncommutative probability space. This is the attempt to explain and observe the combinatorial-object-depending probabilistic structure.
Caffarelli's contraction theorem states that the Brenier optimal transport map from the standard Gaussian measure to a more log-concave probability measure is 1-Lipschitz. Owing to its many applications in analysis, probability, and…
We study the statistical mechanics of a general Hamiltonian system in the context of symplectic structure of the corresponding phase space. This covariant formalism reveals some interesting correspondences between properties of the phase…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
This article, which is substantially motivated by the previous joint work with J. McKay [8], establishes the analytic analogues of the relations we found free probability has with Witt vectors. Therefore, we first present a novel analytic…