inoltro per problemi tecnici grazie alessandra ---------- Forwarded message --------- Da: One World Probability ow.probability@gmail.com Date: gio 28 gen 2021 alle ore 15:03 Subject: Re: [owps] One World Probability Seminar Thursday January 28, 2021 To: owps@lists.bath.ac.uk

Dear All,

If you have trouble joining the meeting using the zoom link below, please try using the link on the website.

We apologise for any problems. Amanda and Alessandra

On Wed, Jan 27, 2021 at 8:26 AM One World Probability < ow.probability@gmail.com> wrote:

Tomorrow's speakers in the One World Probability Seminar are (Note: all times are in UTC. *Due to time changes, you should check what that translates to in your location*)

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(14:00-15:00 UTC) Speaker: Cristina Toninelli (Université Paris Dauphine) Title: Universality results for interacting particle systems with dynamical constraints Abstract: We introduce the kinetically constrained models (KCM), a class of interacting particle systems with a simple spin flip dynamics subject to local dynamical constraints. Each vertex is resampled (independently) at rate one by tossing a (1-q)-coin iff a certain neighbourhood of the vertex contains no particles. In other words, the holes (empty vertices) act as facilitating sites. When q shrinks to 0, the presence of the constraints gives rise to glassy dynamics, in particular to an anomalous divergence of the characteristic time scales. Thus, KCM are extensively used in physics literature to model the liquid-glass transition, a longstanding open problem in condensed matter physics.

We focus on the behavior of E(T_0), the mean over the stationary process of the first time at which the origin becomes empty. Our results establish the universality classes of KCM in two dimensions: we group all possible constraints into distinct classes with all models in a class featuring the same divergence for E(T_0) as q->0. Within each class, we present an efficient relaxation mechanism that involves the cooperative motion of large rare patches of empty sites and we use it to determine matching upper and lower bounds for E(T_0).

Joint work with L.Marêché, I.Hartarsky, F.Martinelli and R.Morris

(15:00-16:00 UTC) Fabio Martinelli (Università Roma Tre) Title: Sharp threshold for the FA-2f kinetically constrained model Abstract: The Fredrickson-Andersen 2-spin facilitated model (FA-2f) on the d-dimensional lattice, d ≥ 2, is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring "dynamical facilitation", an important mechanism in condensed matter physics. In FA-2f a site may change its state only if at least two of its nearest neighbors are empty. The process, while reversible w.r.t. a product Bernoulli measure, has degenerate jumps rates and it is non-attractive, with an anomalous divergence of characteristic time scales as the density q of the empty sites tends to zero. A natural random variable encoding the above features is the first time T at which the origin becomes empty for the stationary process. Our main result is the sharp threshold T ≍ Exp[ d λ(d,2)/q^(1/(d-1)) ] w.h.p. as q → 0, with λ(d,2) the threshold constant for the 2-neighbor bootstrap percolation, the monotone deterministic cellular automaton counterpart of FA-2f. This is the first sharp result for a critical KCM. Besides settling various controversies accumulated in the physics literature over the last four decades, our novel techniques enable completing the recent ambitious program on the universality phenomenon for critical KCM and establishing sharp thresholds for other two-dimensional KCM.

Joint work with I. Hartarski and C. Toninelli

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The zoom link will appear the day before on the OWPS website: https://www.owprobability.org/one-world-probability-seminar https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.owprobability.org%2Fone-world-probability-seminar&data=04%7C01%7Cowps%40lists.bath.ac.uk%7Cd35b573820914b4c4c5408d8c394c728%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637474393069227010%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=dCzcZDFeiUOPoRg%2FJrGgmdu1mbhSG1dwZRdV%2Ba0jmtc%3D&reserved=0

It can also be directly accessed through the link below: https://uniroma1.zoom.us/j/83154591101?pwd=dkZyekxwa1Z1b2w2bW5SOWY3L21Xdz09 https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Funiroma1.zoom.us%2Fj%2F84008096626%3Fpwd%3DN3MyYUFaMElvazIrS3hzNE1aSnRRZz09&data=04%7C01%7Cowps%40lists.bath.ac.uk%7Cd35b573820914b4c4c5408d8c394c728%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637474393069236966%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=VjcnwqCIMLhncn8hInOJXnPtmxcLPngtGZhtvBkAdmI%3D&reserved=0

Please feel free to circulate this email.

We hope to see you all tomorrow! One World Probability Team