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作者：Chen, Wei-Kuo
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The validity of the Parisi formula in the Sherrington-Kirkpatrick model (SK) was initially proved by Talagrand [Ann. of Math. (2) 163 (2006) 221263]. The central argument relied on a dedicated study of the coupled free energy via the two-dimensional Guerra-Talagrand (GT) replica symmetry breaking bound. It is believed that this bound and its higher dimensional generalization are highly related to the conjectures of temperature chaos and ultrametricity in the SK model, but a complete investigat...
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作者：Cotar, Codina; Thacker, Debleena
作者单位：University of London; University College London; Lund University
摘要：In this paper, we introduce a new simple but powerful general technique for the study of edge- and vertex-reinforced processes with super-linear reinforcement, based on the use of order statistics for the number of edge, respectively of vertex, traversals. The technique relies on upper bound estimates for the number of edge traversals, proved in a different context by Cotar and Limic [Ann. AppL Probab. 19 (2009) 1972-2007] for finite graphs with edge reinforcement. We apply our new method both...
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作者：Peled, Ron
作者单位：Tel Aviv University
摘要：A homomorphism height function on the d-dimensional torus Z(n)(d) is a function on the vertices of the torus taking integer values and constrained to have adjacent vertices take adjacent integer values. A Lipschitz height function is defined similarly but may also take equal values on adjacent vertices. For each of these models, we consider the uniform distribution over all such functions with predetermined values at some fixed vertices (boundary conditions). Our main result is that in high di...
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作者：Buckdahn, Rainer; Li, Juan; Peng, Shige; Rainer, Catherine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bretagne Occidentale; Shandong University; Shandong University
摘要：In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data (t,x)is an element of[0,T]xR(d), which coefficients depend on both the solution X-s(t,x) but also its law. By considering square integrable random variables xi as initial condition for this equation, we can easily show the flow property of the solution X-s(t,xi) of this new equation. Associating it with a process X-s(t,x,P xi) which coincides with X-s(t,xi), when one ...
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作者：Martineau, Sebastien; Tassion, Vincent
作者单位：Weizmann Institute of Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that the value of the critical probability for percolation on an Abelian Cayley graph is determined by its local structure. This is a partial positive answer to a conjecture of Schramm: the function pc defined on the set of Cayley graphs of Abelian groups of rank at least 2 is continuous for the Benjamini-Schramm topology. The proof involves group-theoretic tools and a new block argument.
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作者：Barlow, M. T.; Croydon, D. A.; Kumagai, T.
作者单位：University of British Columbia; University of Warwick; Kyoto University
摘要：The first main result of this paper is that the law of the (rescaled) two-dimensional uniform spanning tree is tight in a space whose elements are measured, rooted real trees continuously embedded into Euclidean space. Various properties of the intrinsic metrics, measures and embeddings of the subsequential limits in this space are obtained, with it being proved in particular that the Hausdorff dimension of any limit in its intrinsic metric is almost surely equal to 8/5. In addition, the tight...
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作者：Auffinger, Antonio; Chen, Wei-Kuo
作者单位：Northwestern University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.
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作者：Basse-O'Connor, Andreas; Lachieze-Rey, Raphael; Podolskij, Mark
作者单位：Aarhus University; Universite Paris Cite
摘要：In this paper, we present some new limit theorems for power variation of kth order increments of stationary increments Levy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while the time span remains fixed, the asymptotic theory gives novel results, which (partially) have no counterpart in the theory of discrete moving averages. More specifically, we show that the first-order limit theory and the mode of convergence strongly depend on th...
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作者：Obloj, Jan; Spoida, Peter
作者单位：University of Oxford
摘要：We solve the n-marginal Skorokhod embedding problem for a continuous local martingale and a sequence of probability measures mu(1),...,mu(n) which are in convex order and satisfy an additional technical assumption. Our construction is explicit and is a multiple marginal generalization of the Azema and Yor [In Seminaire de Probabilites, XIII (Univ. Strasbourg, Strasbourg, 1977/78) (1979) 90-115 Springer] solution. In particular, we recover the stopping boundaries obtained by Brown, Hobson and R...
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作者：Campese, Simon
作者单位：University of Rome Tor Vergata
摘要：We prove a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. [Ann. Prob. 38 (2010) 396-438] and Rosen [Stoch. Dyn. 11 (2011) 5-48], which were later reproven by Hu and Nualart [Electron. Commun. Probab. 15 (2010) 396-410] and Rosen [In Seminaire de Probabilites XLIII (2011) 95-104 Springer] are included. Furthermore, a conjecture of Rosen for the fourth moment is settled: In comparison...
