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作者：Dianetti, Jodi; Ferrari, Giorgio; Fischer, Markus; Nendel, Max
作者单位：University of Bielefeld; University of Padua
摘要：We study mean field games with scalar Ito-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences. First, it allows us to prove existence of solutions via an application of Tarski's fixed point theorem, covering cases with discontinuous dependence on the measure variable. Second, it ensures that the set of solutions enjoys a lattice structure: in particular, there...
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作者：Ernst, Philip A.; Franceschi, Sandro
作者单位：Rice University; Universite Paris Saclay
摘要：Let pi be the occupancy density of an obliquely reflected Brownian motion in the half plane and let (rho, alpha) be the polar coordinates of a point in the upper half plane. This work determines the exact asymptotic behavior of pi(rho, alpha) as rho -> infinity with alpha epsilon (0, pi). We find explicit functions a, b, c such that pi(rho, alpha) similar to(rho -> infinity) a(alpha) rho(b(alpha)) e(-c(alpha)rho). This closes an open problem first stated by Professor J. Michael Harrison in Aug...
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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...
