相关论文: Traffic Distributions and Independence II: Univers…
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by…
We study random band matrices within the framework of traffic probability, an operadic non-commutative probability theory introduced by Male based on graph operations. As a starting point, we revisit the familiar case of the permutation…
For any tracial non-commutative probability space $(\mathcal{A}, \varphi)$, C\'{e}bron, Dahlqvist, and Male showed that one can always construct an enveloping traffic space $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$ that extends the trace.…
Traffic congestion, a daily frustration for millions and a multi-billion dollar drain on economies, has long resisted deep physical understanding. While simple theoretical models of traffic flow have suggested connections to critical…
Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss…
In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the…
We construct non-commutative analogs of transport maps among free Gibbs state satisfying a certain convexity condition. Unlike previous constructions, our approach is non-perturbative in nature and thus can be used to construct transport…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
We prove the free analogue of the transportation cost inequality for tracial distributions of non-commutative self-adjoint (also unitary) multi-variables based on random matrix approximation procedure.
The $\mathcal{A}$-tracial algebras are algebras endowed with multi-linear forms, compatible with the product, and indexed by partitions. Using the notion of $\mathcal{A}$-cumulants, we define and study the $\mathcal{A}$-freeness property…
We study a mass transport model on a ring with parallel update, where a continuous mass is randomly redistributed along distinct links of the lattice, choosing at random one of the two partitions at each time step. The redistribution…
Motivated by recent work of Au, C{\'e}bron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
The concept of resilience can be realized in natural and engineering systems, representing the ability of system to adapt and recover from various disturbances. Although resilience is a critical property needed for understanding and…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
Statistical traffic data analysis is a hot topic in traffic management and control. In this field, current research progresses focus on analyzing traffic flows of individual links or local regions in a transportation network. Less attention…
Let $(\sigma_N^{(i)})_{i \in I}$ be a family of symmetric permutations of the entries of a Wigner matrix $\mathbf{W}_N$. We characterize the limiting traffic distribution of the corresponding family of dependent Wigner matrices…
Many-particle simulations of vehicle interactions have been quite successful in the qualitative reproduction of observed traffic patterns. However, the assumed interactions could not be measured, as human interactions are hard to quantify…
The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and…
The congestion formation on a urban road network is one of the key issue for the development of a sustainable mobility in the future smart cities. In this work we propose a reductionist approach studying the stationary states of a simple…