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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Sakanaveeti, Akshay
作者单位：University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
摘要：We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the infinite vector of microscopic type-densities and characterizations of the limits as infinite-dimensional conditionally Gaussian processes in a certain Banach space. (b) Functional (joint) central limit theorems for macroscopic observables of the giant component in...
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作者：Lis, Marcin; Rey, Lucas; Ryan, Kieran
作者单位：Technische Universitat Wien; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider two different versions of the double dimer model on a planar domain, where we either fold a single dimer cover on a symmetric domain onto itself across the line of symmetry, or we superimpose two independent dimer covers on two, almost identical, domains that differ only on a certain portion of the boundary. This results in a collection of loops and doubled edges that, unlike in the classical double dimer case of Kenyon, are accompanied by arcs emanating from the line of symmetry o...
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作者：Bass, Richard F.; Burdzy, Krzysztof
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：Consider the deterministic Skorokhod equation in the closed first quadrant: X-t=x(0)+f(t)+integral(t)(0)v(X-s)dL(s), where f:[0,infinity)-> R-2 is a continuous function, f(0)=0, X-t takes values in the quadrant for all t, and L-t is a process that starts at 0, is non-decreasing and continuous, and increases only at those times when is on the boundary of the quadrant. Suppose v on the positive x axis, equals (1,-a(2)) on the positive y axis, and v(0) points into the closed first quadrant. Let t...
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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
摘要：In long-range percolation on Z(d), we connect each pair of distinct points x and y by an edge independently at random with probability 1-exp(-beta parallel to x-y parallel to(-d-alpha)), where alpha> 0 is fixed and beta >= 0 is a parameter. In a previous paper, we proved that if 0 < alpha < d then the critical two-point function satisfies the spatially averaged upper bound 1/ r(d) & sum;(d)( x is an element of[-r,r]) (P)beta(c)(0 <-> x) <= r(-d+alpha) for every r >= 1. This upper bound is beli...
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Bonn; Imperial College London; University of Cambridge
摘要：We investigate the bond percolation model on transient weighted graphs G induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an extension of Lupu's formula for the two-point function at criticality. We then focus on the low-dimensional case 0 < nu < (alpha)/(2) , where alpha governs the polynomial volume growth of G and nu the decay rate of the Green's function on G. In particul...
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Sakanaveeti, Akshay
作者单位：University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
摘要：We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the infinite vector of microscopic type-densities and characterizations of the limits as infinite-dimensional conditionally Gaussian processes in a certain Banach space. (b) Functional (joint) central limit theorems for macroscopic observables of the giant component in...
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作者：Lis, Marcin; Rey, Lucas; Ryan, Kieran
作者单位：Technische Universitat Wien; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider two different versions of the double dimer model on a planar domain, where we either fold a single dimer cover on a symmetric domain onto itself across the line of symmetry, or we superimpose two independent dimer covers on two, almost identical, domains that differ only on a certain portion of the boundary. This results in a collection of loops and doubled edges that, unlike in the classical double dimer case of Kenyon, are accompanied by arcs emanating from the line of symmetry o...
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作者：Bass, Richard F.; Burdzy, Krzysztof
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：Consider the deterministic Skorokhod equation in the closed first quadrant: X-t=x(0)+f(t)+integral(t)(0)v(X-s)dL(s), where f:[0,infinity)-> R-2 is a continuous function, f(0)=0, X-t takes values in the quadrant for all t, and L-t is a process that starts at 0, is non-decreasing and continuous, and increases only at those times when is on the boundary of the quadrant. Suppose v on the positive x axis, equals (1,-a(2)) on the positive y axis, and v(0) points into the closed first quadrant. Let t...
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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
摘要：In long-range percolation on Z(d), we connect each pair of distinct points x and y by an edge independently at random with probability 1-exp(-beta parallel to x-y parallel to(-d-alpha)), where alpha> 0 is fixed and beta >= 0 is a parameter. In a previous paper, we proved that if 0 < alpha < d then the critical two-point function satisfies the spatially averaged upper bound 1/ r(d) & sum;(d)( x is an element of[-r,r]) (P)beta(c)(0 <-> x) <= r(-d+alpha) for every r >= 1. This upper bound is beli...
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Bonn; Imperial College London; University of Cambridge
摘要：We investigate the bond percolation model on transient weighted graphs G induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an extension of Lupu's formula for the two-point function at criticality. We then focus on the low-dimensional case 0 < nu < (alpha)/(2) , where alpha governs the polynomial volume growth of G and nu the decay rate of the Green's function on G. In particul...
