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Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

机译:通过组合插值进行稀释自旋系统的复制品界限

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In two papers Franz et al. proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution (Franz and Leone in J Stat Phys 111(3–4):535–564, 2003) and a general distribution (Franz et al. in J Phys A 36(43), 10967, 2003). Panchenko and Talagrand (Probab Theo Relat Fields 130(3):319–336, 2004) simplified the proof and generalized the result of Franz and Leone (J Stat Phys 111(3–4):535–564, 2003) for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks (Salez in Combin Probab Comput 25(03):436–447, 2016) and allows to bypass the arguments in Franz et al. (J Phys A 36(43):10967, 2003) based on the study of the Sherrington–Kirkpatrick (SK) model.
机译:在两篇论文Franz等人。 证明了稀释随机约束的自由能量的污染满足问题,用于泊松度分布(J STEM Phys 111(3-4)中的Franz和Leone 111(3-4):535-564,2003)和一般分布(Franz等人。在J. 物理A 36(43),10967,2003)。 Panchenko和Talagrand(Probab Theo Relat领域130(3):319-336,2004)简化了Franz和Leone的证据和广泛性(J STEM PHORE 111(3-4):535-564,2003)的泊松 案件。 我们为一般程度分配案例提供了一个新的证据,并作为一种推论,我们在大规模的随机常规图中获得了最大独立集(也称为硬核模型)的新界限。 我们的证据使用基于偏见随机漫步的组合插值(Combin Probab Comput 25(03):436-447,2016)并允许绕过Franz等人的参数。 (J Proma 36(43):10967,2003)基于Sherrington-Kirkpatrick(SK)模型的研究。

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