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作者：Djete, Mao Fabrice
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we provide convergence and existence results for mean field games of controls. Mean field games of controls are a class of mean field games where the mean field interactions are achieved through the joint (conditional) distribution of the controlled state and the control process. The framework we are considering allows to control the diffusion coefficient & sigma;, and the controls/strategies are supposed to be of open loop type. Using (con-trolled) Fokker-Planck equations, we i...
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作者：Erdos, Laszlo; Krueger, Torben; Enfrew, David
作者单位：University of Erlangen Nuremberg; State University of New York (SUNY) System; Binghamton University, SUNY
摘要：We consider the long time asymptotic behavior of a large system of N linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our previous work (SIAM J. Math. Anal. 50 (2018) 3271-3290) that was restricted to the independent case. In particular, we analyze a recent model in the theory of neural networks (Phys. Rev. E 97 (2018) 062314) that specifically focused on the effect of the distr...
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作者：Wu, Yihong; Xu, Jiaming; Yu, Sophie H.
作者单位：Yale University; Duke University
摘要：We study the problem of detecting the edge correlation between two ran-dom graphs with n unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated; under the alternative, the two graphs are edge-correlated under some latent node correspondence, but have the same marginal distributions as the null. For both Gaussian-weighted complete graphs and dense Erd6s- Renyi graphs (with edge probability n-o(1)), we dete...
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作者：Fehrman, Benjamin
作者单位：University of Oxford
摘要：We provide a proof of stochastic homogenization for random environ-ments with a mean zero, divergence-free drift. We prove that the environ-ment homogenizes weakly in H1 if the drift admits a stationary L2-integrable stream matrix, and we prove that the two-scale expansion converges strongly in H1 if the drift admits a stationary Ld & PROVES;(2+& delta; )-integrable stream matrix. Ad-ditionally, under this stronger integrability assumption, we show that the en-vironment almost surely satisfies...
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作者：Cosso, Andrea; Gozzi, Fausto; Kharroubi, Idris; Pham, Huyen; Rosestolato, Mauro
作者单位：University of Milan; Luiss Guido Carli University; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; University of Salento
摘要：We study the optimal control of path-dependent McKean-Vlasov equa-tions valued in Hilbert spaces motivated by non-Markovian mean-field mod-els driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we prove the dynamic programming principle (DPP) in such a general framework. The crucial law invariance property of the value function V is rigorously obtained, which means that V can be viewed as a function on the Wasserstein space of probability measures ...
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作者：Bello, Jason; Sivakoff, David J.
作者单位：University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：We study the cyclic cellular automaton (CCA) and the Greenberg- Hastings model (GHM) with & kappa; & GE; 3 colors and contact threshold & theta; & GE; 2 on the infinite (d + 1)-regular tree, Td. When the initial state has the uniform product distribution, we show that these dynamical systems exhibit at least two distinct phases. For sufficiently large d, we show that if & kappa; (& theta; - 1) & LE; d - O(& RADIC;d & kappa; ln(d)), then every vertex almost surely changes its color infinitely o...
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作者：Caragea, Andrei; Petersen, Philipp; Voigtlaender, Felix
作者单位：University of Vienna
摘要：We prove bounds for the approximation and estimation of certain binary classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guarantees for empirical risk minimization us-ing networks of a suitable size, depending on the number of training samples available. The obtained approximation and estimation rates are independent of the dimension of the input, showing that the curse of dimensionality can be overcome in this setting; in fact, the input d...
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作者：Shen, Hao; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Wisconsin System; University of Wisconsin Madison; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this paper we study the perturbation theory of ?42 model on the whole plane via stochastic quantization. We use integration by parts formula (i.e., Dyson-Schwinger equations) to generate the perturbative expansion for the k-point correlation functions, and prove bounds on the remainder of the trun-cated expansion using PDE estimates; this in particular proves that the ex-pansion is asymptotic. Furthermore, we derive short distance behaviors of the 2-point function and the connected 4-point ...
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作者：Henning, Florian; Kuelske, Christof
作者单位：Ruhr University Bochum
摘要：We provide an existence theory for gradient Gibbs measures for Z-valued spin models on regular trees which are not invariant under translations of the tree, assuming only summability of the transfer operator. The gradient states we obtain are delocalized. The construction we provide for them starts from a two-layer hidden Markov model representation in a setup which is not invari-ant under tree-automorphisms, involving internal q-spin models. The proofs of existence and lack of translation inv...
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作者：Lacker, Daniel; Le Flem, Luc
作者单位：Columbia University
摘要：This paper studies the convergence problem for mean field games with common noise. We define a suitable notion of weak mean field equilibria, which we prove captures all subsequential limit points, as n & RARR; & INFIN;, of closed -loop approximate equilibria from the corresponding n-player games. This ex-tends to the common noise setting a recent result of the first author, while also simplifying a key step in the proof and allowing unbounded coefficients and non-i.i.d. initial conditions. Co...
