Related papers: Traffic Distributions and Independence II: Univers…
We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
We propose three models for the traffic of vehicles within a network formed by sites (cities, car-rental agencies, parking lots, etc.) and connected by two-way arteries (roads, highways), that allow forecasting the vehicular flux in a…
Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…
Understanding how cities transition from free-flowing to congested traffic remains a central open problem in urban science. Here we show that city-scale congestion undergoes a reproducible nonlinear transition analogous to an order-disorder…
As a dynamical complex system, traffic is characterized by a transition from free flow to congestions, which is mostly studied in highways. However, despite its importance in developing congestion mitigation strategies, the understanding of…
Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…
This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
We consider two extensions of free probability that have been studied in the research literature, and are based on the notions of c-freeness and respectively of infinitesimal freeness for noncommutative random variables. In a 2012 paper,…
We study the analysis of all the movements of the population on the basis of their mobility from one node to another, to observe, measure, and predict the impact of traffic according to this mobility. The frequency of congestion on roads…
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional…
We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…
We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…
In this note we prove a Birkhoff type transitivity theorem for continuous maps acting on non-separable completely metrizable spaces and we give some applications for dynamics of bounded linear operators acting on complex Fr\'{e}chet spaces.…
In this paper, we present our work on clustering and prediction of temporal dynamics of global congestion configurations in large-scale road networks. Instead of looking into temporal traffic state variation of individual links, or of small…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…