-
作者：Le Gall, Jean-Francois; Riera, Armand
作者单位：Universite Paris Cite
摘要：We provide a unified approach to the three main non-compact models of random geometry, namely the Brownian plane, the infinite-volume Brownian disk, and the Brownian half-plane. This approach allows us to investigate relations between these models, and in particular to prove that complements of hulls in the Brownian plane are infinite-volume Brownian disks.
-
作者：Barlow, M. T.; Croydon, D. A.; Kumagai, T.
作者单位：University of British Columbia; Kyoto University
摘要：This article investigates the heat kernel of the two-dimensional uniform spanning tree. We improve previous work by demonstrating the occurrence of log-logarithmic fluctuations around the leading order polynomial behaviour for the on-diagonal part of the quenched heat kernel. In addition we give two-sided estimates for the averaged heat kernel, and we show that the exponents that appear in the off-diagonal parts of the quenched and averaged versions of the heat kernel differ. Finally, we deriv...
-
作者：Duminil-Copin, Hugo; Manolescu, Ioan; Tassion, Vincent
作者单位：University of Geneva; Universite Paris Saclay; University of Fribourg; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：This paper is studying the critical regime of the planar random-cluster model on Z(2) with cluster-weight q is an element of [1, 4). More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on their extremal lengths. They imply in particular that any fractal boundary is touched by macroscopic clusters, uniformly in its roughness or the configuration on the boundary. Additionally, they imply that any sub-sequential scaling limit of the ...
-
作者：Lubetzky, Eyal; Sly, Allan
作者单位：New York University; Princeton University
摘要：In the study of Markov chain mixing times, analysis has centered on the performance from a worst-case starting state. Here, in the context of Glauber dynamics for the one-dimensional Ising model, we show how new ideas from information percolation can be used to establish mixing times from other starting states. At high temperatures we show that the alternating initial condition is asymptotically the fastest one, and, surprisingly, its mixing time is faster than at infinite temperature, acceler...
-
作者：Barraquand, Guillaume; Corwin, Ivan; Dimitrov, Evgeni
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Columbia University
摘要：We prove that the free energy of the log-gamma polymer between lattice points (1, 1) and (M, N) converges to the GUE Tracy-Widom distribution in the M-1/3 scaling, provided that N/M remains bounded away from zero and infinity. We prove this result for the model with inverse gamma weights of any shape parameter theta > 0 and furthermore establish a moderate deviation estimate for the upper tail of the free energy in this case. Finally, we consider a non i.i.d. setting where the weights on finit...
-
作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：We study long-range Bernoulli percolation on Z(d) in which each two vertices x and y are connected by an edge with probability 1 - exp(-beta parallel to x - y parallel to(-d-alpha)). It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if 0 < alpha < d then there is no infinite cluster at the critical parameter beta(c). We give a new, quantitative proof of this theorem establishing the power-law upper bound P-beta c (vertical bar K vertical bar >= n) <= Cn(-(d-alpha)/(2d+alpha)) for...
-
作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University
-
作者：Miller, Jason; Sheffield, Scott; Werner, Wendelin
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble CLE kappa' for kappa' in (4, 8) that is drawn on an independent gamma-LQG surface for gamma(2) = 16/kappa'. The results are similar in flavor to the ones from our companion paper dealing with CLE kappa for kappa in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the CLE kappa' in te...
-
作者：Caravenna, Francesco; den Hollander, Frank
作者单位：University of Milano-Bicocca; Leiden University - Excl LUMC; Leiden University
摘要：We consider a directed polymer of length N interacting with a linear interface. The monomers carry i.i.d. random charges (omega(i))(i=1)(N) taking values in R with mean zero and variance one. Each monomer i contributes an energy (beta omega(i) - h)phi(S-i) to the interaction Hamiltonian, where S-i is an element of Z is the height of monomer i with respect to the interface, phi : Z -> [0, infinity) is the interaction potential, beta is an element of [0, infinity) is the inverse temperature, and...
