Friday 3 May 2024 at Augsburg University

Schedule:

14:00    Get-together with coffee and cookies

14:30    Talk Chengcheng Ling 

16:00    Talk Jack Hanson

Titles and abstracts:

Chengcheng Ling: Regularization by noise and approximations of singular kinetic SDEs

Regularisation by noise in the context of stochastic differential equations (SDEs) with coefficients of low regularity, known as singular SDEs, refers to the beneficial effect produced by noise so that the singularity from the coefficients is smoothed out yielding well-behaved equations. Kinetic SDEs, also sometimes called second order SDEs, as one typical type of stochastic Hamiltonian systems, describe the motion of a particle perturbed by some random external force. The difference of comparing it with usual SDEs is that the noise of the space position vanishes and only appears in the direction of velocity, hence less noise gets involved in the system. In this talk we will discuss about the regularization effect by the degenerate noise for the singular kinetic SDEs from numerical approximation and also particles approximation view point.

Jack Hanson: Robust construction of the high-dimensional incipient infinite cluster

In Bernoulli percolation, the incipient infinite cluster (IIC) is a version of the "open cluster of the origin at criticality conditioned to be infinite". Since this event should have probability 0 on Z^d, the IIC is constructed via a limiting procedure. For d > 6, several constructions have been given and shown to produce the same object, but many natural limiting procedures remain unexplored. For instance, it is an open question whether conditioning on {0 is connected to the boundary of [-n, n]^d} produces the IIC as n tends to infinity. We answer this question in the affirmative as a corollary of our theorem, which roughly says "conditioning on any long open connection produces the IIC", and whose proof does not directly use lace expansion analysis.