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作者：Maillard, Pascal
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider branching Brownian motion on the real line with the following selection mechanism: every time the number of particles exceeds a (large) given number N, only the N right-most particles are kept and the others killed. After rescaling time by , we show that the properly recentred position of the -th particle from the right, , converges in law to an explicitly given spectrally positive L,vy process. This behaviour has been predicted to hold for a large class of models falling into the ...
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作者：Fribergh, Alexander; Kious, Daniel
作者单位：Universite de Montreal; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider elliptic random walks in i.i.d. random environments on . The main goal of this paper is to study under which ellipticity conditions local trapping occurs. Our main result is to exhibit an ellipticity criterion for ballistic behavior which extends previously known results. We also show that if the annealed expected exit time of a unit hypercube is infinite then the walk has zero asymptotic velocity.
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作者：Lacker, Daniel
作者单位：Princeton University
摘要：The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may be asymmetric and based on full information. It is shown that approximate Nash equilibria in the n-player games admit certain weak limits as n tends to infinity, and every limit is a weak solution of the mean field game (MFG). Conversely, every weak MFG solu...
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作者：Sabot, Christophe; Tarres, Pierre
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; CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon-Nikodym derivative of the reversed vertex-reinforced jump process measure with respect to the Markov jump process with the same conductances. Next we show that a variant of this process provides an inversion of that Ray-Knight identity. We give a similar result for the Ray-Knight first generalized Theorem.
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作者：Rohde, Steffen; Zhan, Dapeng
作者单位：University of Washington; University of Washington Seattle; Michigan State University
摘要：The backward chordal Schramm-Loewner evolution naturally defines a conformal welding homeomorphism of the real line. We show that this homeomorphism is invariant under the automorphism , and conclude that the associated solution to the welding problem (which is a natural renormalized limit of the finite time Loewner traces) is reversible. The proofs rely on an analysis of the action of analytic circle diffeomorphisms on the space of hulls, and on the coupling techniques of the second author.
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作者：Kenyon, Richard W.; Sun, Nike; Wilson, David B.
作者单位：Brown University; Stanford University; Microsoft
摘要：We study asymptotics of the dimer model on large toric graphs. Let be a weighted -periodic planar graph, and let be a large-index sublattice of . For bipartite we show that the dimer partition function on the quotient has the asymptotic expansion where A is the area of , is the free energy density in the bulk, and is a finite-size correction term depending only on the conformal shape of the domain together with some parity-type information. Assuming a conjectural condition on the zero locus of...
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作者：Chatterjee, Shirshendu
作者单位：City University of New York (CUNY) System; City College of New York (CUNY)
摘要：We consider a model for heterogeneous gene regulatory networks that is a generalization of the model proposed by Chatterjee and Durrett (Random Struct Algorithms 39(2):228-246, 2011) as an annealed approximation of Kauffmann's (J Theor Biol 22(3):437-467, 1969) random Boolean networks. In this model, genes are represented by the vertices of a random directed graph on n vertices having specified in-degree distribution (resp. joint distribution of in-degree and out-degree), and the expression bi...
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作者：Terhesiu, Dalia
作者单位：University of Vienna
摘要：We obtain higher order theory for the long term behavior of the transfer operator associated with the unit interval map if , if for the whole range , which corresponds to the infinite measure preserving case. Higher order theory for is more challenging and requires new techniques. Along the way, we provide higher order theory for scalar and operator renewal sequences with infinite measure and regular variation. Although the present work considers the unit interval map mentioned above as a toy ...
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作者：Donoho, David; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：In a recent article, El Karoui et al. (Proc Natl Acad Sci 110(36):14557-14562, 2013) study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n. Using numerical simulations and 'highly plausible' heuristic arguments, they unveil a striking new phenomenon. Namely, the regression coefficients contain an extra Gaussian noise component that is not explained by classical concepts such as the Fisher informa...
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作者：Karatzas, Ioannis; Ruf, Johannes
作者单位：Columbia University; University of London; University College London
摘要：We study the distribution of the time to explosion for one-dimensional diffusions. We relate this question to the computation of expectations of suitable nonnegative local martingales. Moreover, we characterize the distribution function of the time to explosion as the minimal solution to a certain Cauchy problem for an appropriate parabolic differential equation; this leads to alternative characterizations of Feller's criterion for explosions. We discuss in detail several examples for which it...
