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作者：Bella, Peter; Fehrman, Benjamin; Otto, Felix
作者单位：Leipzig University; Max Planck Society
摘要：We study the behavior of second-order degenerate elliptic systems in divergence form with random coefficients which are stationary and ergodic. Assuming moment bounds like Chiarini and Deuschel (2014) on the coefficient field a and its inverse, we prove an intrinsic large-scale C-1,C-alpha-regularity estimate for a-harmonic functions and obtain a first-order Liouville theorem for a-harmonic functions.
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作者：Chen, Wei-Kuo; Panchenk, Dmitry
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Toronto
摘要：We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: K-spin antiferromagnetic Ising model for even K >= 2, K-spin spin glass model for even K >= 2, and random K-sat model for all K >= 2. We show that modifying even a small proportion of clauses results in near maximizers of the original and modified Hamiltonians being nearly orthogonal to each other with high probability. We use a standard technique of approximating diluted models by ...
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作者：Chen, Yu-Ting
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We investigate stochastic spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the one-dimensional Wright-Fisher diffusions. Convergence in the Wasserstein distance of the laws of the occupation measures also holds. The proofs study the convergences under certain voter models by an equivalence between their laws and the laws of the ev...
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作者：Bhamidi, Shankar; Jin, Jimmy; Nobel, Andrew
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution and small world distance scaling. In this context, a natural question is how to understand the effect of change points-how abrupt changes in parameters driving the network model change structural properties of the network. We study this phenomenon in one po...
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作者：Gnedin, Alexander; Iksanov, Alexander; Marynych, Alexander; Moehle, Martin
作者单位：University of London; Queen Mary University London; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; Eberhard Karls University of Tubingen
摘要：Lambda-coalescents model the evolution of a coalescing system in which any number of blocks randomly sampled from the whole may merge into a larger block. For the coalescent restricted to initially n singletons, we study the collision spectrum (X-n,X- k : 2 <= k <= n), where X-n,X- k counts, throughout the history of the process, the number of collisions involving exactly k blocks. Our focus is on the large n asymptotics of the joint distribution of the X-n,X- k's, as well as on functional lim...
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作者：Mourrat, Jean-Christophe; Valesin, Daniel
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); University of Groningen
摘要：Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with small average graph distance between vertices, but adding an edge comes at a cost measured according to the geometry of the ambient physical space. In most cases, we identify the order of magnitude of the average graph distance as a function of the parameters...
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作者：Fernholz, E. Robert; Karatzas, Ioannis; Ruf, Johannes
作者单位：Columbia University; University of London; London School Economics & Political Science
摘要：in an equity market consisting of a fixed number d of assets with capitalization weights mu(i) (.), is an observable and a nondecreasing function of time. If this observable of the market is not just nondecreasing but actually grows at a rate bounded away from zero, then strong arbitrage can be constructed relative to the market over sufficiently long time horizons. It has been an open issue for more than ten years, whether such strong outperformance of the market is possible also over arbitra...
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作者：Campi, Luciano; Fischer, Markus
作者单位：University of London; London School Economics & Political Science; University of Padua
摘要：We introduce a simple class of mean-field games with absorbing boundary over a finite time horizon. In the corresponding N-player games, the evolution of players' states is described by a system of weakly interacting Ito equations with absorption on first exit from a bounded open set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean-field game,...
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作者：Mangoubi, Oren; Smith, Aaron
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Ottawa
摘要：We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold M, which we call the geodesic walk. We prove that the mixing time of this walk on any manifold with positive sectional curvature C-x(u, v) bounded both above and below by 0 < m(2) <= C-x(u, v) <= M-2 <( )infinity is O*(M-2/m(2)). In particular, this bound on the mixing time does not depend explicitly on the dimension of the manifold. In the special case that M is the boundary of a convex body, we gi...
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作者：Jacod, Jean; Todorov, Viktor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Northwestern University
摘要：We derive limit theorems for functionals of local empirical characteristic functions constructed from high-frequency observations of Ito semimartingales contaminated with noise. In a first step, we average locally the data to mitigate the effect of the noise, and then in a second step, we form local empirical characteristic functions from the pre-averaged data. The final statistics are formed by summing the local empirical characteristic exponents over the observation interval. The limit behav...
