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作者：Chen, Xin; Kumagai, Takashi; Wang, Jian
作者单位：Shanghai Jiao Tong University; Kyoto University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：We study the quenched invariance principle for random conductance models with long range jumps on Z(d), where the transition probability from x to y is, on average, comparable to vertical bar x - y vertical bar(-(d+alpha)) with alpha is an element of (0, 2) but is allowed to be degenerate. Under some moment conditions on the conductance, we prove that the scaling limit of the Markov process is a symmetric alpha-stable Levy process on R-d. The well-known corrector method in homogenization theor...
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作者：Chleboun, Paul; Smith, Aaron
作者单位：University of Warwick; University of Ottawa
摘要：Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in ( J. Stat. Phys. 169 (2017) 441-471). Our main result is that the plaquette model with periodic boundary conditions, on this length scale, exhibits a sharp transition in the convergence to equilibrium, known as cutoff...
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作者：Hofmanova, Martina; Leahy, James-Michael; Nilssen, Torstein
作者单位：University of Bielefeld; Imperial College London; University of Agder
摘要：We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of strong solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Mor...
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作者：Davies, Sami; Racz, Miklos Z.; Rashtchian, Cyrus
作者单位：University of Washington; University of Washington Seattle; Princeton University; University of California System; University of California San Diego
摘要：We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. For many classes of trees, including complete trees and spiders, we provide algorithms that reconstruct the labels using only a polynomial number of traces. This exhibits a stark contrast to known results on string trace reconstruction, which req...
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作者：Mitsche, Dieter; Penrose, Mathew D.
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Bath
摘要：In the random geometric graph G(n, r(n)), n vertices are placed randomly in Euclidean d-space and edges are added between any pair of vertices distant at most r(n) from each other. We establish strong laws of large numbers (LLNs) for a large class of graph parameters, evaluated for G(n, r(n)) in the thermodynamic limit with nr(n)(d) = const., and also in the dense limit with nr(n)(d) -> infinity, r(n) -> 0. Examples include domination number, independence number, clique-covering number, eterna...
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作者：Wang, Andi Q.; Pollock, Murray; Roberts, Gareth O.; Steinsaltz, David
作者单位：University of Bristol; Newcastle University - UK; University of Warwick; University of Oxford
摘要：We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution as their invariant measures, thus making them amenable for use within Monte Carlo methodologies. Since the regeneration mechanism can compensate the choice of local dynamics, while retaining the same invariant distribution, great flexibility can be achieved i...
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作者：Chen, Wei-Kuo; Handschy, Madeline; Lerman, Gilad
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider a spiked random tensor obtained as a mixture of two components: noise in the form of a symmetric Gaussian p-tensor for p >= 3 and signal in the form of a symmetric low-rank random tensor. The latter is defined as a linear combination of k independent symmetric rank-one random tensors, referred to as spikes, with weights referred to as signal-to-noise ratios (SNRs). The entries of the vectors that determine the spikes are i.i.d. sampled from general probability distributions supported ...
