Resumen: Quantum decoherence (QD) is today one cornerstone in the development of quantum computing (QC). This refers to the collapse of a quantum state into a classical one. From a mathematical point of view, its modelling has also been a major problem, motivating the development of new research in open systems theory. One could classify today this phenomenon at the interface between non-commutative and commutative probabilities. The general question is: how a quantum evolution becomes classical? Is this inevitable? Shall QC live with that? The talk will provide a panorama on the...Read More
Resumen: We shall discuss functional CLTs for additive functionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels of which the first one is a Brownian motion with a well-known covariance matrix. However, in the second level we see a new feature: it is the iterated integral of the same Brownian motion perturbed by a deterministic linear function called the area anomaly and characterized in terms of the model. With that one obtains sharper information on the limiting path. The construction of new examples for SDE...Read More
Error Bounds for the One-Dimensional Constrained Langevin Approximation for Density Dependent Markov Chains.
Resumen: The stochastic dynamics of chemical reaction networks are often modeled using continuous-time Markov chains. However, except in very special cases, these processes cannot be analysed exactly and their simulation can be computationally intensive. An approach to this problem is to consider a diffusion approximation. The Constrained Langevin Approximation (CLA) is a reflected diffusion approximation for stochastic chemical reaction networks proposed by Leite & Williams. In this work, we extend this approximation to (nearly) density dependent Markov chains, when the diffusion state...Read More
Resumen: We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass. We provide a theoretical analysis of this object and discuss its interpretation in the light of convex ordering between probability measures. In particular, we show that, rather than averaging in a geometric way the input distributions, as the Wasserstein barycenter based on classic optimal transport does, weak barycenters extract common geometric information shared by all the input distributions, encoded as a latent random variable that...Read More
Resumen: Lattice trees is a probabilistic model for random subtrees of . In this talk we are going to review some previous results about the convergence of lattice trees to the “Super-Brownian motion” in the high-dimensional setting. Then, we are going to show some new theorems which strengthen the topology of said convergence. Finally, if time permits, we will discuss the applications of these results to the study of random walks on lattice trees. Joint work with A. Fribergh, M. Holmes and E. Perkins.Read More