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作者：Escauriaza, Luis; Schwarz, Daniel C.; Xing, Hao
作者单位：University of Basque Country; University of London; University College London; Boston University
摘要：Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in Z. Using unique continuation and backward uniqueness, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.
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作者：Berger, Noam; Procaccia, Eviatar B.; Turner, Amanda
作者单位：Technical University of Munich; Technion Israel Institute of Technology; University of Leeds
摘要：We construct and study a stationary version of the Hastings-Levitov(0) model. We prove that, unlike in the classical HL(0) model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL(0) is proposed as a potential candidate for a stationary off-lattice variant of diffusion limited aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finitenes...
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作者：Ehrlacher, Virginie; Lelievre, Tony; Monmarche, Pierre
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Paris Cite; Sorbonne Universite
摘要：We analyze and propose variants of the adaptive biasing force method. First, we prove the convergence of a version of the algorithm where the biasing force is estimated using a weighted occupation measure, with an explicit asymptotic variance. Second, we propose a new flavour of the algorithm adapted to high-dimensional reaction coordinates, for which the standard approaches suffer from the curse of dimensionality. More precisely, the free energy is approximated by a sum of tensor products of ...
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作者：Noack, Christian; Sosoe, Philippe
作者单位：Cornell University
摘要：Seppalainen and Valko showed in (ALEA Lat. Am. J. Probab. Math. Stat. 7 (2010) 451-476) that for a suitable choice of parameters, the variance growth of the free energy of the stationary O'Connell-Yor polymer is governed by the exponent 2/3, characteristic of models in the KPZ universality class. We develop exact formulas based on Gaussian integration by parts to relate the cumulants of the free energy, log Z(n,t)(theta), to expectations of products of quenched cumulants of the time of the fir...
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作者：Coja-Oghlan, Amin; Mueller, Noela; Ravelomanan, Jean B.
作者单位：Dortmund University of Technology; Eindhoven University of Technology
摘要：Corroborating a prediction from statistical physics, we prove that the belief propagation message passing algorithm approximates the partition function of the random k-SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as replica symmetry in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random k-SAT model...
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作者：Fredes, Luis; Linker, Amitai; Remenik, Daniel
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Universidad Andres Bello; Universidad de Chile; Universidad de Chile
摘要：We investigate the effect on survival and coexistence of introducing forest fire epidemics to a certain two-species competition model. The model is an extension of the one introduced by Durrett and Remenik (Ann. Appl. Probab. 19 (2009) 1656-1685), who studied a discrete time particle system running on a random 3-regular graph where occupied sites grow until they become sufficiently dense so that an epidemic wipes out large clusters. In our extension we let two species affected by independent e...
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作者：Campi, Luciano; De Angelis, Tiziano; Ghio, Maddalena; Livieri, Giulia
作者单位：University of Milan; University of Turin; Collegio Carlo Alberto; Scuola Normale Superiore di Pisa
摘要：We study Nash equilibria for a sequence of symmetric N-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface that splits the state space into action and inaction regions. We then show that a solution of the MFG of capacity expansion induces approximate Nash equi...
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作者：Jain, Vishesh; Pillai, Natesh S.; Sah, Ashwin; Sawhney, Mehtaab; Smith, Aaron
作者单位：Stanford University; Harvard University; Massachusetts Institute of Technology (MIT); University of Ottawa
摘要：In this work, we analyze dimension reduction algorithms based on the Kac walk and discrete variants. (1) For n points in R-d, we design an optimal Johnson-Lindenstrauss (JL) transform based on the Kac walk which can be applied to any vector in time O(d log d) for essentially the same restriction on n as in the best-known transforms due to Ailon and Liberty, and Bamberger and Krahmer. Our algorithm is memory-optimal, and outperforms existing algorithms in regimes when n is sufficiently large an...
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作者：Kious, Daniel; Mailler, Cecile; Schapira, Bruno
作者单位：University of Bath; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：It is well known in biology that ants are able to find shortest paths between their nest and the food by successive random explorations, without any mean of communication other than the pheromones they leave behind them. This striking phenomenon has been observed experimentally and modelled by different mean-field reinforcement-learning models in the biology literature. In this paper, we introduce the first probabilistic reinforcement-learning model for this phenomenon. In this model, the ants...
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作者：Fang, Rongjuan; Li, Zenghu
作者单位：Fujian Normal University; Beijing Normal University
摘要：A continuous-state branching process in varying environments is constructed by the pathwise unique positive solution to a stochastic integral equation driven by time-space noises. The cumulant semigroup of the process is characterized in terms of a backward integral equation. We clarify the behavior of the process at its bottlenecks, which are the deterministic times when it arrives at zero almost surely by negative jumps. The process arises naturally as the scaling limit of Galton-Watson proc...
