Titlebook: In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius; Maria Eulália Vares,Roberto Fernández,Charles M. N Book 2021 The Editor(s) (

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On the Four-Arm Exponent for 2D Percolation at Criticality,trongest so far being ., where .. denotes the two-arm exponent). We first briefly discuss five proofs (some of them implicit and not self-contained) from the literature. Then we observe that, by combining two of them, one gets a completely self-contained (and yet quite short) proof.

斗志

Universality of Noise Reinforced Brownian Motions,e is to establish a version of Donsker’s invariance principle for a large family of step-reinforced random walks in the diffusive regime, and more specifically, to show that . arises as the universal scaling limit of the former. This extends known results on the asymptotic behavior of the so-called elephant random walk.

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Geodesic Rays and Exponents in Ergodic Planar First Passage Percolation, shape is the .. ball and that there are exactly four infinite geodesics starting at the origin a.s. In addition we determine the exponents for the variance and wandering of finite geodesics. We show that the variance and wandering exponents do not satisfy the relationship of .?=?2.???1 which is expected for independent first passage percolation.

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Upper Bounds on the Percolation Correlation Length,e that the correlation length, both below and above criticality, is bounded from above by .. Improving on this bound would be a further step towards the conjecture that there is no infinite cluster at criticality on . for every .?≥?2.

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1050-6977 Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas‘ interests and contributions to probability theory.978-3-030-60756-2978-3-030-60754-8Series ISSN 1050-6977 Series E-ISSN 2297-0428

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between the two sometimes disjoint approaches available in the literature, the ring theoretic approach, and the homological algebra approach. The book covers most results in commutative coherent ring theory known to date, as well as a number of results never published before. Starting with elementa