AMSS概率论及相关领域报告

Fall 2022 / 2022年秋

Jean-François Le Gall (Université Paris-Saclay)
2022-09-28, Wednesday, 15:00 – 16:00 (Beijing time)
南楼N204，Zoom 827 3397 0965 (passcode: amss2022)
Title: Recent developments in random geometry
Abstract: Models of two-dimensional random geometry are obtained as universal scaling limits in the Gromov-Hausdorff sense of large graphs embedded in the sphere. These models, which include the Brownian sphere, the Brownian disk and the Brownian plane, are also closely related to the quantum surfaces studied by Miller and Sheffield. We will present recent progress in the study of these random metric spaces. In particular we will discuss some remarkable properties of geodesics and mention some open problems.
Jean Bertoin (University of Zurich)
2022-10-13, Thursday, 15:00 – 16:00 (Beijing time)
南楼N620, Zoom 834 9592 9584, passcode: amss2022
Title: A model for an epidemic with contact tracing and cluster isolation, and a detection paradox
Abstract: We determine the distributions of some random variables related to a simple model of an epidemic with contact tracing and cluster isolation and compute explicitly the asymptotic proportion of isolated clusters with a given size amongst all isolated clusters, conditionally on survival of the epidemic. Somewhat surprisingly, the latter differs from the distribution of the size of a typical cluster at the time of its detection; and we explain the reasons behind this seeming paradox.
Matthias Winkel (University of Oxford)
2022-10-25, Tuesday, 15:00 – 16:00 (Beijing time)
南楼N620, Zoom 894 4481 9443 (Pin: amss2022)
Title: The Aldous diffusion
Abstract: Motivated by an up-down Markov chain on cladograms, David Aldous conjectured in 1999 that there exists a “diffusion on continuum trees” whose mass partitions at any finite number of branchpoints evolve as certain Wright-Fisher diffusions with some negative mutation rates, until some branchpoint disappears. We construct this conjectured process via a consistent system of stationary evolutions of binary trees with k labelled leaves and edges decorated with diffusions on a space of interval partitions. This pathwise construction allows us to study and compute path properties of this “Aldous diffusion,” including evolutions of projected masses and distances between branch points. The continuum-tree-valued Aldous diffusion has the (simple) Markov property and is path-continuous. If there is time, I will discuss the failure of the strong Markov property. This is joint work, partly in progress, with Noah Forman, Soumik Pal and Douglas Rizzolo.
Yueyun Hu 胡跃云 (Université Sorbonne Paris Nord)
2022-11-10, Thursday, 15:00 – 16:00 (Beijing time)
南楼N620, Zoom 886 9890 2888, Passcode: amss2022
Title: On the Derrida-Retaux recursive model
Abstract: In order to study the depinning transition in presence of strong disorder, Derrida and Retaux (J. Stat. Phys. (2014)) introduced a discrete-time max-type recursive model. It is believed that for a large class of recursive models, including the Derrida and Retaux model, there are highly non-trivial universalities on the critical behavior of the free energy. In this talk, we will review some recent results and open questions on the Derrida and Retaux model as well as on its continuous-time version. The talk is based on joint works with Xinxing Chen, Victor Dagard, Bernard Derrida, Mikhail Lifshits, Bastien Mallein, Michel Pain and Zhan Shi.
Wendelin Werner (ETH Zurich)
2022-11-23, Wednesday, 15:00 – 16:00 (Beijing time)
南楼N620, Zoom 890 4721 6511 (Pin: amss2022)
Title: From Marc Yor to Brownian loop-soups
Abstract: We will survey aspects of Brownian loop-soups, which provide a higher-dimensional incarnation of some ideas present Marc Yor‘s works.