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The sensitivity of anomalous transport in crowded media to the form of the inter-particle interactions is investigated through computer simulations. We extend the highly simplified Lorentz model towards realistic natural systems by modeling…
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth…
In this communication, complex systems with a near trivial dynamics are addressed. First, under the hypothesis of equiprobability in the asymptotic equilibrium, it is shown that the (hyper) planar geometry of an $N$-dimensional multi-agent…
This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…
We revisit the classic problem of determining optimal routes in a graph for transporting two given distributions defined on its nodes, originally studied by Wardrop and Beckmann in the 1950s. The global congestion profile at any given time…
We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional law given the observation of the target, we characterize…
We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
This paper gives a constructive treatment of McKenzie's theorem on the existence of general equilibria. While the full theorem does not admit a constructive proof, and hence does not admit a computational realisation, we show that if we…
We model parking in urban centers as a set of parallel queues and overlay a game theoretic structure that allows us to compare the user-selected (Nash) equilibrium to the socially optimal equilibrium. We model arriving drivers as utility…
We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for…
We study competitive equilibrium in the canonical Fisher market model, but with indivisible goods. In this model, every agent has a budget of artificial currency with which to purchase bundles of goods. Equilibrium prices match between…
Flextime is one of the efficient approaches in travel demand management to reduce peak hour congestion and encourage social distancing in epidemic prevention. Previous literature has developed bi-level models of the work starting time…
Congestion pricing has long been hailed as a means to mitigate traffic congestion; however, its practical adoption has been limited due to the resulting social inequity issue, e.g., low-income users are priced out off certain roads. This…
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…
The introduction of autonomous (self-driving) and shared autonomous vehicles (AVs and SAVs) will affect travel destinations and distances, mode choice, and congestion. From a traffic perspective, although some congestion reduction may be…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
We develop a Schumpeterian quality-ladder spatial model in which innovation arrivals depend on regional knowledge spillovers. A parsimonious reduced-form diffusion mechanism induces the convergence of regions' average distance to the global…
We consider a dynamical system with finitely many equilibria and perturbed by small noise, in addition to being controlled by an `expensive' control. The controlled process is optimal for an ergodic criterion with a running cost that…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…