-
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...
-
作者：Friz, Peter K.; Zorin-Kranich, Pavel
作者单位：Technical University of Berlin; University of Bonn
摘要：We establish a new scale of p-variation estimates for martingale para-products, martingale transforms and Ito integrals, of relevance in rough paths theory, stochastic and harmonic analysis. As an application, we introduce rough semimartingales, a common generalization of classical semimartin-gales and (controlled) rough paths and their integration theory.
-
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.
-
作者：Priola, Enrico
作者单位：University of Pavia
-
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...
-
作者：Muirhead, Stephen; Rivera, Alejandro; Vanneuville, Hugo; Kohler-Schindler, Laurin
作者单位：University of London; Queen Mary University London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of positive associations (also known as the 'FKG inequality'), and hence many classical arguments in percolation theory do not apply. More precisely, we consider a smooth stationary centred planar Gaussian field f and, given a level l epsilon R, we study the connectivity properties of the excursion set {f >= -l}. We prove th...
-
作者：Blumenthal, Alex; Zelati, Michele Coti; Gvalani, Rishabh S.
作者单位：University System of Georgia; Georgia Institute of Technology; Imperial College London; Max Planck Society
摘要：We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that allows us to construct space-time smooth, uniformly bounded in time, universal exponential mixers. The framework is then applied to the problem of proving exponential mixing in a classical example proposed by Pierrehumbert in 1994, consisting of alternating periodic shear flows with randomized phases. This settles a ...
-
作者：Subag, Eliran
作者单位：Weizmann Institute of Science
摘要：In a companion paper we developed the generalized TAP approach for general multispecies spherical mixed p-spin models. In this paper we use it to compute the limit of the free energy at any temperature for all pure mul-tispecies spherical p-spin models, assuming that certain free energies con-verge. Importantly, the pure multispecies models do not satisfy the convexity assumption on the mixture which was crucial in the recent proofs of the Parisi formula for the multispecies Sherrington-Kirkpa...
-
作者：Hofmanova, Martina; 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：We are concerned with the three-dimensional incompressible Navier- Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in L2 we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, solving one of the open problems in the field. This result, in partic-ular, implies nonuniqueness in law. Second, we prove nonuniqueness of the associated Markov processes in a suitably...
-
作者：Kozma, Gady; Samotij, Wojciech
作者单位：Weizmann Institute of Science; Tel Aviv University
摘要：We show that the naive mean-field approximation correctly predicts the leading term of the logarithmic lower tail probabilities for the number of copies of a given subgraph in G(n, p) and of arithmetic progressions of a given length in random subsets of the integers in the entire range of densities where the mean-field approximation is viable.Our main technical result provides sufficient conditions on the maximum degrees of a uniform hypergraph ?-L that guarantee that the logarithmic lower tai...
