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作者：Gwynne, Ewain; Pfeffer, Joshua; Park, Minjae
作者单位：University of Chicago; Columbia University
摘要：We study the Loewner evolution whose driving function is W-t = B-t(1) + iB(t)(2), where (B-1, B-2) is a pair of Brownian motions with a given covariance matrix. This model can be thought of as a generalization of Schramm-Loewner evolution (SLE) with complex parameter values. We show that our Loewner evolutions behave very differently from ordinary SLE. For example, if neither B-1 nor B-2 is identically equal to zero, then the set of points disconnected from infinity by the Loewner hull has non...
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：The critical 2d stochastic heat flow (SHF) is a stochastic process of ran-dom measures on R2, recently constructed in (Invent. Math. 233 (2023) 325- 460). We show that this process falls outside the class of Gaussian multiplica-tive chaos (GMC), in the sense that it cannot be realised as the exponential of a (generalised) Gaussian field. We achieve this by deriving strict lower bounds on the moments of the SHF that are of independent interest.
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作者：Priola, Enrico
作者单位：University of Pavia
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作者：Taggia, Lorenzo
作者单位：Sapienza University Rome
摘要：We prove that in wide generality the critical curve of the activated random walk model is a continuous function of the deactivation rate, and we provide a bound on its slope, which is uniform with respect to the choice of the graph. Moreover, we derive strict monotonicity properties for the probability of a wide class of increasing events, extending previous results of (Invent. Math. 188 (2012) 127-150). Our proof method is of independent interest and can be viewed as a reformulation of the 'e...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik; Xu, Yuanyuan
作者单位：Princeton University; Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n x n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.
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作者：Addario-Berry, Louigi; Barrett, Jordan
作者单位：McGill University
摘要：We consider invasion percolation on the complete graph K-n, started from some number k(n) of distinct source vertices. The outcome of the process is a forest consisting of k(n) trees, each containing exactly one source. Let M-n be the size of the largest tree in this forest. Logan, Molloy and Pralat (2018) proved that if k(n)/n(1/3)-> 0 then M-n/n -> 1 in probability. In this paper, we prove a complementary result: if k(n)/n(1/3)-> infinity, then M-n/n -> 0 in probability. This establishes the...
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作者：Contat, Alice; Curien, Nicolas
作者单位：Universite Paris Saclay
摘要：Consider a uniform rooted Cayley tree T-n with n vertices and let m cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its arrival node, and if the spot is already occupied, it drives towards the root of the tree and parks as soon as possible. Lackner and Panholzer (J. Combin. Theory Ser. A 142 (2016) 1-28) established a phase transition for this process when m approximate to n/2. In this work, we couple this model with a variant of the classical ...
