1st: 2020-03-06: Budapest /// 2nd: 2020-09-22: Vienna - on Zoom /// 3rd: 2021-09-30: Budapest ///
4th: 2022-04-27: Vienna /// 5th: 2023-03-17: Budapest /// 6th: 2023-10-06: Vienna ///
Venue: Rényi Insitute Budapest, Lecture Room (first floor)
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Outbound trains Wien Hbf --> Budapest Keleti: 07:40 - 10:19 /// 08:42 - 11:19 /// 09:40 - 12:19
Abstract: The sample paths of most stochastic processes are rather oscillatory. One of the interesting consequences of this property is that additive functionals of such processes enjoy a lot of cancellation/averaging. This regularisation phenomenon of the noise has been long of interest in connection to local times, skew processes, quadrature problems, fluid dynamics, or stochastic quantisation. We overview some old and new approaches in stochastic and pathwise analysis to study these regularising effects.
Abstract: We consider long range percolation on Z^d in a finite box of volume n in dimension d. In this model edges are independently present between any tow vertices x,y with probability constant times 1/|x-y|^(alpha d). When the multiplying constant is large enough, the model is supercritical, and there is an infinite component of density theta = Prob( the origin is part of the infinite component); which then intuitively suggests the existence of a giant component in a finite box; having density roughly theta. In this talk we study large deviation for this giant component; and show that it undergoes a dichotomy: the lower tail Prob( largest component < n (theta-epsilon)) has polynomial speed in the volume while the upper tail Prob( largest component > n (theta+epsilon) ) has linear speed. If one modifies the model to allow for inhomogeneous vertex marks, (e.g. as in geometric inhomogeneous random graphs or the Poisson Boolean model with random radii); then the lower tail remains to have polynomial speed, but the upper tail becomes much heavier. The speed is `log n'; and we can express the exact rate function using the (inverse of the) generating function of the cluster of the origin in the infinite model. Joint work with Joost Jorritsma and Dieter Mitsche.
Abstract: With the conceptual aim of optimizing Markov chains in one way or another for better mixing, we analyze random directed graphs according to a multitype configurational model. To this end, we allow tuning the transition probabilities corresponding to the types. Our goal is to understand the impact on mixing achieved through this flexibilty, together with the observed cutoff phenomenon. Joint work with John Fernley.
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Participants who wish to stay overnight in Budapest are kindly asked to make their own arrangements for accommodation.