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作者：Ding, Jian; Fukushima, Ryoki; Sun, Rongfeng; Xu, Changji
作者单位：University of Pennsylvania; Kyoto University; National University of Singapore; University of Chicago
摘要：Place an obstacle with probability 1 - p independently at each vertex of Z(d) , and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. For d >= 2 and p strictly above the critical threshold for site percolation, we condition on the environment such that the origin is contained in an infinite connected component free of obstacles. It has previously been shown that, with high probability, the random walk conditioned on survival up to time n will be localize...
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作者：Basu, Riddhipratim; Ganguly, Shirshendu; Hammond, Alan
作者单位：Tata Institute of Fundamental Research (TIFR); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：In last passage percolation models lying in the Kardar-Parisi-Zhang universality class, maximizing paths that travel over distances of order n accrue energy that fluctuates on scale n(1/3); and these paths deviate from the linear interpolation of their endpoints on scale n(2/3). These maximizing paths and their energies may be viewed via a coordinate system that respects these scalings. What emerges by doing so is a system indexed by x, y is an element of R and s, t is an element of R with s <...
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作者：Fan, Zhou; Mei, Song; Montanari, Andrea
作者单位：Yale University; University of California System; University of California Berkeley; Stanford University; Stanford University
摘要：We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional estimation problem known as Z(2) synchronization. Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free e...
