Dear colleagues, I am glad to announce the following hybrid probability seminar with *two* *speakers* at Milano-Bicocca. Date and time: *Thursday September 7, 10:00-12:00 *(Rome time, zone)*, * *Aula 3014* Building *U5*/RATIO, Univ. *Milano-Bicocca*. Zoom link: https://us02web.zoom.us/j/84444882953?pwd=QkVweTJ4RDJMamN3cjExblViUExMZz09 ID riunione: *844 4488 2953, *Passcode: *835623* *10:00-11:00 Marco Carfagnini (*University of California San Diego) Title: Spectral gaps via small deviations. Abstract: In this talk we will discuss spectral gaps of second order differential operators and their connection to limit laws such as small deviations and Chung’s laws of the iterated logarithm. The main focus is on hypoelliptic diffusions such as the Kolmogorov diffusion and horizontal Brownian motions on Carnot groups. If time permits, we will discuss spectral properties and existence of spectral gaps on general Dirichlet metric measure spaces.This talk is based on joint works with Maria (Masha) Gordina and Alexander (Sasha) Teplyaev. *11:00-12:00 Willem Van Zuijlen* (Weierstrass Institute Berlin) Title: Weakly self avoiding walk in a random potential. Abstract: We investigate a model of simple-random walk paths in a random environment that has two competing features: an attractive one towards the highest values of a random potential, and a self-repellent one in the spirit of the well-known weakly self-avoiding random walk. We tune the strength of the second effect such that they both contribute on the same scale as the time variable tends to infinity. In this talk I will discuss our results on the identification of (1) the logarithmic asymptotics of the partition function, and (2) of the path behaviour that gives the overwhelming contribution to the partition function. This is joint work with Wolfgang König, Nicolas Pétrélis and Renato Soares dos Santos. Best regards, Tal Orenshtein -- Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca https://sites.google.com/site/talorenshtein314159/