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作者：Schapira, Bruno; Valesin, Daniel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; University of Groningen
摘要：We consider the contact process on finite and connected graphs and study the behavior of the extinction time, that is, the amount of time that it takes for the infection to disappear in the process started from full occupancy. We prove, without any restriction on the graph G, that if the infection rate is larger than the critical rate of the one-dimensional process, then the extinction time grows faster than for any constant , where |G| denotes the number of vertices of G. Also for general gra...
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作者：Izyurov, Konstantin
作者单位：University of Helsinki
摘要：We prove a general result on convergence of interfaces in the critical planar Ising model to conformally invariant curves absolutely continuous with respect to SLE(3). Our setup includes multiple interfaces on arbitrary finitely connected domains, and we also treat the radial SLE case. In the case of simply and doubly connected domains, the limiting processes are described explicitly in terms of rational and elliptic functions, respectively.
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作者：Miller, Jason; Wu, Hao
作者单位：University of Cambridge; University of Geneva
摘要：We compute the almost-sure Hausdorff dimension of the double points of chordal for , confirming a prediction of Duplantier-Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of chordal for as well as analogous dimensions for the radial and whole-plane processes for . We derive these facts as consequences of a more general result in which we compute the dimension of the intersection of two flow lines of the formal vector field , where h is a Gaussian...
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作者：Asselah, Amine; Schapira, Bruno
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the boundary of the range of simple random walk on in the transient case . We show that volumes of the range and its boundary differ mainly by a martingale. As a consequence, we obtain an upper bound on the variance of order in dimension three. We also establish a Central Limit Theorem in dimension four and larger.
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作者：Dembo, Amir; Mukherjee, Sumit
作者单位：Stanford University; Columbia University
摘要：Suppose the auto-correlations of real-valued, centered Gaussian process are non-negative and decay as for some regularly varying at infinity of order . With its primitive, we show that the persistence probabilities decay rate of is precisely of order , thereby closing the gap between the lower and upper bounds of Newell and Rosenblatt (Ann. Math. Stat. 33:1306-1313, 1962), which stood as such for over fifty years. We demonstrate its usefulness by sharpening recent results of Sakagawa (Adv. App...
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作者：Oh, Tadahiro; Tzvetkov, Nikolay
作者单位：University of Edinburgh; Heriot Watt University; University of Edinburgh; CY Cergy Paris Universite
摘要：We consider the cubic fourth order nonlinear Schrodinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces , , are quasi-invariant under the flow.
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作者：Sinclair, Alistair; Srivastava, Piyush; Stefankovic, Daniel; Yin, Yitong
作者单位：University of California System; University of California Berkeley; California Institute of Technology; University of Rochester; Nanjing University
摘要：We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model (which is defined as a weighted sum over all matchings where each matching is given a weight in terms of a fixed parameter called the monomer activity) and the hard core model (which is defined as a weighted sum over all independent sets where an independent...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. In Georgiou et al. (Probab Theory Relat Fields, 2016, doi:10.1007/s00440-016-0729-x) we constructed stationary cocycles and Busemann functions for this model. Using these objects, we prove new results on the competition interface, on existence, uniqueness, and coalescence of directional semi-infi...
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作者：Friz, Peter K.; Shekhar, Atul
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Technical University of Berlin
摘要：Existence of Loewner trace is revisited. We identify finite energy paths (the skeleton of Wiener measure) as natural class of regular drivers for which we find simple and natural estimates in terms of their (Cameron-Martin) norm. Secondly, now dealing with potentially rough drivers, a representation of the derivative of the (inverse of the) Loewner flow is given in terms of a rough- and then pathwise Follmer integral. Assuming the driver within a class of It-processes, an exponential martingal...
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作者：Liu, Yuan
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：It is known that a quadratic transportation-information inequality interpolates between the Talagrand's inequality and the log-Sobolev inequality (LSI for short). The aim of this paper is threefold: (1) To prove the equivalence of and the Lyapunov condition, which gives a new characterization inspired by Cattiaux et al. (Probab Theory Relat Fields 148(1-2):285-304, 2010). (2) To prove the stability of under bounded perturbations, which gives a transference principle in the sense of Holley-Stro...
