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 /// 7th: 2024-03-08: Budapest /// 8th: 2024-10-04: Vienna /// 9th: 2025-03-28: Budapest /// 10th: 2025-10-10: Vienna
Venue: Renyi Institute
Outbound trains Wien Hbf --> Budapest Keleti : 07:40 - 10:20 /// 08:40 - 11:20 /// 09:40 - 12:20
Title: On the scaling limit of interfaces in the critical planar Ising model perturbed by a magnetic field
Abstract: In this talk, I will present some recent results on the scaling limit of interfaces in the critical planar Ising model perturbed by a magnetic field. I will first consider the case when the field is a deterministic function. In this case, I will show that in the so-called near-critical regime and when the Ising model has Dobrushin boundary conditions, the interface separating +1 and -1 spins has a scaling limit whose law is conformally covariant and absolutely continuous with respect to SLE3. Its limiting law is a massive version of SLE3 in the sense of Makarov and Smirnov. I will also discuss the scaling limit of this interface when the magnetic perturbation is not near-critical.
In the second part of the talk, I will discuss some ongoing work with Fenglin Huang and Aoteng Xia in which we look at the case when the magnetic field is given by a collection of iid centered Gaussian random variables, one for each vertex. In this setting, in the near-critical regime, we show that almost surely in the disorder, the scaling limit of the quenched law of the ±1 interface is absolutely continuous with respect to SLE3. We then show that this contrasts with the scaling limit of the quenched law of the collection of nested spin loops, which turns out to be almost surely singular with respect to nested CLE3. This also contrasts with the deterministic case where it is known that in the near-critical regime, any subsequential limit of the collection of nested spin loops is absolutely continuous with respect to nested CLE3.
Title: Loop soups in 2 + epsilon dimensions
Abstract: We consider a natural percolation model built from the so-called Brownian loop soup. We will give sense to studying its phase transition in dimension d = 2 + epsilon, with epsilon varying in [0,1], and discuss how to perform a rigorous „epsilon-expansion“ in this context. Our approach gives access to a continuous family of universality classes, and elucidates the behaviour of critical exponents etc. near the (lower-)critical dimension, which for this model is d=2. Based on joint works with Wen Zhang.
Title: Activated random walk and self-organized criticality
Abstract: Activated random walk (ARW) is a stochastic particle system and toy model of self-organized criticality (SOC), a phenomenon widely observed in real-world systems that was first described heuristically by physicists Bak, Tang and Wiesenfeld in the late 1980s. Based on computer simulations, ARW is widely believed to exhibit the key features of SOC -- universality, critical power law scaling, and hyperuniformity -- in a robust way. Additionally, among the many proposed toy models of SOC, ARW has proven to be the most tractable due to its abelian property and generous use of independent randomness. Despite these benefits, fully establishing the predictions of SOC for ARW remains an elusive goal, even in dimension one. I will discuss recent results which pave the way toward SOC, and mention a recently conjectured probabilistic property of ARW which suggests a new path forward.
Dinner information will be announced closer to the event date.
Participants who wish to stay overnight in Budapest are kindly asked to make their own arrangements for accommodation.
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