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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Cambridge; Imperial College London
摘要：We investigate level sets of the Gaussian free field on continuous transient metric graphs g and study the capacity of its level set clusters. We prove, without any further assumption on the base graph G, that the capacity of sign clusters on (G) over tilde is finite almost surely. This leads to a new and effective criterion to determine whether the sign clusters of the free field on (G) over tilde are bounded or not. It also elucidates why the critical parameter for percolation of level sets ...
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作者：Sly, Allan; Sun, Nike; Zhang, Yumeng
作者单位：Princeton University; Massachusetts Institute of Technology (MIT); Stanford University
摘要：Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions of statistical physics. Here we revisit one of these models, random regular k-nae-sat: knowing the satisfiability threshold, it is natural to study, in the satisfiable regime, the number of solutions in a typical instance. We prove here that the...
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作者：El Alaoui, Ahmed; Montanari, Andrea
作者单位：Cornell University; Stanford University
摘要：We consider the problem of estimating a vector of discrete variables theta = (theta(1), ..., theta(n)), based on noisy observations Y-uv of the pairs (theta(u), theta(v)) on the edges of a graph G = ([n], E). This setting comprises a broad family of statistical estimation problems, including group synchronization on graphs, community detection, and low-rank matrix estimation. A large body of theoretical work has established sharp thresholds for weak and exact recovery, and sharp characterizati...
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作者：Andres, Sebastian; Chiarini, Alberto; Slowik, Martin
作者单位：University of Manchester; Eindhoven University of Technology; University of Mannheim
摘要：We establish a quenched local central limit theorem for the dynamic random conductance model on Z(d) only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show Holder continuity estimates for solutions to the heat equation for discrete finite difference operators in divergence form with time-dependent degenerate weights. The proof is based on De Giorgi's iteration technique. In addition, we also derive a quenched local central limit ...
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作者：Benigni, Lucas
作者单位：Universite Paris Cite
摘要：We exhibit new functions of the eigenvectors of the Dyson Brownian motion which follow an equation similar to the Bourgade-Yau eigenvector moment flow (Bourgade and Yau in Commun Math Phys 350(1):231-278, 2017). These observables can be seen as a Fermionic counterpart to the original (Bosonic) ones. By analyzing both Fermionic and Bosonic observables, we obtain new correlations between eigenvectors: (i) The fluctuations n-ary sumation Sigma(alpha is an element of I)|uk(alpha)|2-|I|/N decorrela...
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作者：MacLaurin, James
作者单位：New Jersey Institute of Technology
摘要：We study the dynamics of symmetric and asymmetric spin-glass models of size N. The analysis is in terms of the double empirical process: this contains both the spins, and the field felt by each spin, at a particular time (without any knowledge of the correlation history). It is demonstrated that in the large N limit, the dynamics of the double empirical process becomes deterministic and autonomous over finite time intervals. This does not contradict the well-known fact that SK spin-glass dynam...
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE kappa loop measures for kappa is an element of(0,8). First, we construct rooted SLE kappa loop measures in the Riemann sphere (C) over cap, which satisfy Mobius covariance, conformal Markov property, reversibility, and space-time homogeneity, when the loop is parametrized by its (1+kappa-8) -dimensional Minkowski content. Second, by integrating rooted SLE kappa loop measures, we construct the unro...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We investigate properties of Markov quasi-diffusion processes corresponding to elliptic operators L = a(ij) D-ij + b(i) D-i, acting on functions on R-d, with measurable coefficients, bounded and uniformly elliptic a and b is an element of L-d (R-d). We show that each of them is strong Markov with strong Feller transition semigroup T-t, which is also a continuous bounded semigroup in L-d0 (R-d) for some d(0) is an element of (d/2, d). We show that T-t, t > 0, has a kernel p(t)(x, y) which is su...
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作者：Ebrahimnejad, Farzam; Lee, James R.
作者单位：University of Washington; University of Washington Seattle
摘要：Consider an infinite planar graph with uniform polynomial growth of degree d > 2. Many examples of such graphs exhibit similar geometric and spectral properties, and it has been conjectured that this is necessary. We present a family of counterexamples. In particular, we show that for every rational d > 2, there is a planar graph with uniform polynomial growth of degree d on which the random walk is transient, disproving a conjecture of Benjamini (Coarse Geometry and Randomness, Volume 2100 of...
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作者：Camia, Federico; Jiang, Jianping; Newman, Charles M.
作者单位：New York University; New York University Abu Dhabi; Vrije Universiteit Amsterdam; Yanqi Lake Beijing Institute of Mathematical Sciences & Applications; New York University; New York University; NYU Shanghai
摘要：We study the critical Ising model with free boundary conditions on finite domains in Z(d) with d >= 4. Under the assumption, so far only proved completely for high d, that the critical infinite volume two-point function is of order vertical bar x- y vertical bar(-(d-2)) for large vertical bar x-y vertical bar, we prove the same is valid on large finite cubes with free boundary conditions, as long as x, y are not too close to the boundary. This confirms a numerical prediction in the physics lit...
