作者：Chen, Wei-Kuo
作者单位：University of California System; University of California Irvine
摘要：We consider a spin system obtained by coupling two distinct Sherrington-Kirkpatrick (SK) models with the same temperature and external field whose Hamiltonians are correlated. The disorder chaos conjecture for the SK model states that the overlap under the corresponding Gibbs measure is essentially concentrated at a single value. In the absence of external field, this statement was first confirmed by Chatterjee [Disorder chaos and multiple valleys in spin glasses (2009) Preprint]. In the prese...
作者：del Barrio, Eustasio; Matran, Carlos
作者单位：Universidad de Valladolid
摘要：We consider the problem of optimal incomplete transportation between the empirical measure on an i.i.d. uniform sample on the d-dimensional unit cube [0, 1](d) and the true measure. This is a family of problems lying in between classical optimal transportation and nearest neighbor problems. We show that the empirical cost of optimal incomplete transportation vanishes at rate O-P(n(-1/d)), where n denotes the sample size. In dimension d >= 3 the rate is the same as in classical optimal transpor...
