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作者：Gwynne, Ewain; Sung, Jinwoo
作者单位：University of Chicago
摘要：A Liouville quantum gravity (LQG) surface is a natural random twodimensional surface, initially formulated as a random measure space and later as a random metric space. We show that the LQG measure can be recovered as the Minkowski measure with respect to the LQG metric, answering a question of Gwynne and Miller (Invent. Math. 223 (2021) 213-333). As a consequence, we prove that the metric structure of a gamma -LQG surface determines its conformal structure for every gamma is an element of (0,...
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作者：Maini, Leonardo; Nourdin, Ivan
作者单位：University of Luxembourg
摘要：Let B = (Bx)(x is an element of Rd) be a collection of N(0, 1) random variables forming a real -valued continuous stationary Gaussian field on R-d, and set C(x -y) = E[BxBy]. Let yo : R -> R be such that E[phi(N)(2)] < infinity with N similar to N(0, 1), let R be the Hermite rank of yo, and consider Y-t = integral(tD) phi(B-x)dx, t > 0 with D subset of R-d compact. Since the pioneering works from the 1980s by Breuer, Dobrushin, Major, Rosenblatt, Taqqu and others, central and noncentral limit ...
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作者：Addario-berry, Louigi; Donderwinkel, Serte
作者单位：McGill University; University of Groningen; University of Groningen
摘要：We obtain new nonasymptotic tail bounds for the height of uniformly random trees with a given degree sequence, simply generated trees and conditioned Bienaym & eacute; trees (the family trees of branching processes) in the process settling three conjectures of Janson ( Probab. Surv. 9 (2012) 103-252) and answering several other questions from the literature. Moreover, we define a partial ordering on degree sequences and show that it induces a stochastic ordering on the heights of uniformly ran...
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作者：Usani, Ofer
作者单位：University of Edinburgh
摘要：In exponential last passage percolation, we consider the rescaled Busemann process x bar right arrow N-(1/3) B-0,[xN2/3]e1(rho), x is an element of R, as a process parametrized by the scaled density rho = 1/2+ mu/4 N-1/3, and taking values in C(R). We show that these processes, as N -> infinity, have a right continuous left limit scaling limit G = (G(mu))(mu is an element of R), parametrized by mu and taking values in C(R). The limiting process G, which can be thought of as the Busemann proces...
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作者：Hao, Zimo; Zhang, Xicheng; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Bielefeld; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this paper we study singular kinetic equations on R-2d by the paracontrolled distribution method introduced in Gubinelli, Imkeller and Perkowski (Forum Math. Pi 3 (2015) e6-75). We first develop paracontrolled calculus in the kinetic setting and use it to establish the global well-posedness for the linear singular kinetic equations under the assumptions that the products of singular terms are well defined. We also demonstrate how the required products can be defined in the case that singula...
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作者：Minzer, Dor; Sah, Ashwin; Sawhney, Mehtaab
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove that there exists a constant gamma (crit) approximate to 0.17566 such that if G similar to G (n, 1/2), then for any epsilon > 0 with high probability G has a equipartition such that each vertex has (gamma( crit) - epsilon) root n more neighbors in its own part than in the other part and with high probability no such partition exists for a separation of (gamma( crit) + epsilon) root n . The proof involves a number of tools ranging from isoperimetric results on vertex-transitive sets of...
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作者：Hansen, Benjamin; Mueller, Tobias
作者单位：University of Groningen
摘要：We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster is asymptotically equal to pi A/3 as A-* 0. This answers a question of Benjamini and Schramm ( J. Amer. Math. Soc. 14 (2001) 487-507).
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作者：Dareiotis, Konstantinos; Gerencser, Mate
作者单位：University of Leeds; Technische Universitat Wien
摘要：Differential equations perturbed by multiplicative fractional Brownian motions are considered. Depending on the value of the Hurst parameter H, the resulting equation is pathwise viewed as an ODE, YDE, or RDE. In all three regimes, we show regularisation by noise phenomena by proving the strongest kind of well-posedness with irregular drift: strong existence and path-by-path uniqueness. In the Young and smooth regime H > 1/2, the condition on the drift coefficient is optimal in the sense that ...
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作者：Harris, Simon; Johnston, Samuel g. G.; Pardo, Juan carlos
作者单位：University of Auckland; University of London; King's College London
摘要：Consider a population evolving as a critical continuous-time Galton- Watson (GW) tree. Conditional on the population surviving until a large time T, sample k individuals uniformly at random (without replacement) from amongst those alive at time T. What is the genealogy of this sample of individuals? In cases where the offspring distribution has finite variance, the probabilistic properties of the joint ancestry of these k particles are well J. Probab. 24 (2019) 1-35). In the present article, w...
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作者：Adhikari, Arka; Chatterjee, Sourav
作者单位：Stanford University; Stanford University
摘要：Consider a discrete one-dimensional random surface whose height at a point grows as a function of the heights at neighboring points, plus an independent random noise. Assuming that this function is equivariant under constant shifts, symmetric in its arguments, and at least six times continuously differentiable in a neighborhood of the origin, we show that, as the variance of the noise goes to zero, any such process converges to the Cole-Hopf solution of the 1D KPZ equation under a suitable sca...
