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作者：Sheffield, Scott; Sun, Nike
作者单位：Massachusetts Institute of Technology (MIT); Stanford University
摘要：We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version applies in particular to random lattice paths that have chordal SLE kappa as a scaling limit, with kappa < 8 (nonspace-filling). Existing SLE kappa convergence proofs often begin by showing that the Loewner driving functions of these paths (viewed from infinity) ...
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作者：Miller, Jason; Peres, Yuval
作者单位：Stanford University; Microsoft
摘要：We show that the measure on markings of Z(n)(d), d >= 3, with elements of {0, 1} given by i.i.d. fair coin flips on the range R of a random walk X run until time T and 0 otherwise becomes indistinguishable from the uniform measure on such markings at the threshold T = 1/2 T-cov (Z(n)(d)). a consequence of our methods, we show that the total variation mixing time of the random walk on the lamplighter graph Z(2) (sic) Z(n)(d), d >= 3, has a cutoff with threshold 1/2 T-cov (Z(n)(d)). We give a ge...
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作者：Ioffe, Dmitry; Velenik, Yvan
作者单位：Technion Israel Institute of Technology; University of Geneva
摘要：We consider a model of a polymer in Z(d+1), constrained to join 0 and a hyperplane at distance N. The polymer is subject to a quenched nonnegative random environment. Alternatively, the model describes crossing random walks in a random potential (see Zerner [Ann Appl. Probab. 8 (1998) 246-280] or Chapter 5 of Sznitman [Brownian Motion, Obstacles and Random Media (1998) Springer] for the original Brownian motion formulation). It was recently shown [Ann. Probab. 36 (2008) 1528-1583; Probab. Theo...
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作者：O'Connell, Neil
作者单位：University of Warwick
摘要：We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence.
