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作者：Qian, Zhongmin; Xu, Mingyu
作者单位：University of Oxford; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this article, we study a class of reflected backward stochastic differential equations (introduced in El Karoui et al. [Ann. Probab. 25 (1997) 702-737], RBSDE for short) with nonlinear resistance by means of Skorohod's equation. The advantage of this approach lies in its pathwise nature and, therefore, provides additional information about solutions of RBSDE. As an application of our approach, we will consider reflected backward problems with resistance as well. This class of RBSDEs possess...
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作者：Kiwi, Marcos; Mitsche, Dieter
作者单位：Universidad de Chile; Universidad de Chile; Universite Cote d'Azur
摘要：Random hyperbolic graphs have been suggested as a promising model of social networks. A few of their fundamental parameters have been studied. However, none of them concerns their spectra. We consider the random hyperbolic graph model, as formalized by [Automata, Languages, and Programming-39th International Colloquium-ICALP Part II. (2012) 573-585 Springer], and essentially determine the spectral gap of their normalized Laplacian. Specifically, we establish that with high probability the seco...
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作者：Louart, Cosme; Liao, Zhenyu; Couillet, Romain
作者单位：Universite Paris Saclay
摘要：This article studies the Gram random matrix model G = 1/T Sigma E-T E = sigma (WX), classically found in the analysis of random feature maps and random neural networks, where X = [x(1),, x(T)] epsilon R-PXT is a (data) matrix of bounded norm, W epsilon R-nxp) is a matrix of independent zero-mean unit variance entries and o : R -> R is a Lipschitz continuous (activation) function-sigma (WX) being understood entry-wise. By means of a key concentration of measure lemma arising from nonasymptotic ...
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作者：Fountoulakis, Nikolaos; Kang, Mihyun; Koch, Christoph; Makai, Tamas
作者单位：University of Birmingham; Graz University of Technology; University of Warwick
摘要：A bootstrap percolation process on a graph with infection threshold r >= 1 is a dissemination process that evolves in time steps. The process begins with a subset of infected vertices and in each subsequent step every uninfected vertex that has at least r infected neighbours becomes infected and remains so forever. Critical phenomena in bootstrap percolation processes were originally observed by Aizenman and Lebowitz in the late 1980s as finite-volume phase transitions in Z(d) that are caused ...
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作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University
摘要：The goal of importance sampling is to estimate the expected value of a given function with respect to a probability measure v using a random sample of size n drawn from a different probability measure If the two measures mu and v are nearly singular with respect to each other, which is often the case in practice, the sample size required for accurate estimation is large. In this article, it is shown that in a fairly general setting, a sample of size approximately exp(D(v || mu)) is necessary a...
