-
作者：Helmuth, Tyler; Perkins, Will; Petti, Samantha
作者单位：Durham University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Harvard University
摘要：We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions three and higher. As the dimension tends to infinity, our improvements are by factors of 2 and 1.7, respectively. We make these improvements by utilizing techniques from theoretical computer science to show that a certain Markov chain for sampling from the hard sphere model mixes rapidly at low enough fugacities. We then prove an equivalence between optimal spatial and te...
-
作者：Kolokoltsov, Vassili N.
作者单位：University of Warwick
摘要：In this paper we are merging the two new branches of game theory: quantum games and mean-field games (MFG). Building a quantum analog of MFGs requires the full reconstruction of its foundations and methodology, because in N-particle quantum evolution particles are not separated in individual dynamics and the key concept of the classical MFG theory, the empirical measure defined as the sum of Dirac masses of the positions of the players, is not applicable in quantum setting. As a preliminary re...
-
作者：Horst, Ulrich; Xu, Wei
作者单位：Humboldt University of Berlin; Humboldt University of Berlin
摘要：We provide a general probabilistic framework within which we estab-lish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent Poisson random measures that capture the arrival of exogenous shocks and the arrival of self-excited shocks, respectively. Vari-ous well-studied stochastic volatility models wit...
-
作者：Piatnitski, Andrey; Pirogov, Sergey; Zhizhina, Elena
作者单位：UiT The Arctic University of Tromso; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences
摘要：The paper deals with a family of jump Markov process defined in a medium with a periodic or locally periodic microstructure. We assume that the generator of the process is a zero order convolution type operator with rapidly oscillating locally periodic coefficient and, under natural ellipticity and localization conditions, show that the family satisfies the large deviation principle in the path space equipped with Skorokhod topology. The corre-sponding rate function is defined in terms of a fa...
-
作者：Crawford, Nicholas; Rosenthal, Ron
作者单位：Technion Israel Institute of Technology
摘要：The complex Ginibre ensemble is the distribution of an N x N nonHermitian random matrix over C with i.i.d. complex Gaussian entries normalized to have mean zero and variance 1/N. Unlike the Gaussian unitary ensemble, for which the eigenvectors are distributed according to Haar measure on the compact group U (N), independently of the eigenvalues, the geometry of the eigenbases of the Ginibre ensemble are not particularly well understood. In this paper we systematically study properties of eigen...
-
作者：Cardaliaguet, Pierre; Souganidis, Panagiotis E.
作者单位：Universite PSL; Universite Paris-Dauphine; University of Chicago
摘要：We consider mean field games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution exists and is unique for monotone coupling functions. We also use the solution to find approximate optimal strategies (Nash equilibria) for N-player differential games with common but no idiosyncratic noise. An important step in the analysis is the study of the...
-
作者：Backhoff, Julio; Bartl, Daniel; Beiglbock, Mathias; Wiesel, Johannes
作者单位：University of Twente; University of Vienna; Columbia University
摘要：A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and connections to various areas (e.g., Plug-Pichler-stochastic programming, Hellwig-game theory, Aldous-stability of optimal stopping, Hoover-Keisler-model theory). Remarkably, all these seemingly independent approaches define the same adapted weak topology in finite...
-
作者：Horst, Ulrich; Xia, Xiaonyu; Zhou, Chao
作者单位：Humboldt University of Berlin; Humboldt University of Berlin; Wenzhou University; City University of Hong Kong
摘要：We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semilinear PDE with superlinear gradient, monotone generator and singular terminal value. We also establish an asymptotic analysis of the robust model for small amounts of uncertainty and analyze the effect of robustness on optimal trading strategies and liquidation costs. In...
-
作者：Owada, Takashi
作者单位：Purdue University System; Purdue University
摘要：The objective of this paper is to examine the asymptotic behavior of persistence diagrams associated with Cech filtration. A persistence diagram is a graphical descriptor of a topological and algebraic structure of geometric objects. We consider Cech filtration over a scaled random sample r(n)(-1) chi(n) = {r(n)(-1) x(1), ..., r(n)(-1) X-n}, such that r(n) -> 0 as n -> infinity. We treat per- sistence diagrams as a point process and establish their limit theorems in the sparse regime: nr(n)(d)...
-
作者：Addario-Berry, Louigi; Lin, Jessica; Tendron, Thomas
作者单位：McGill University; University of Oxford
摘要：We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in d dimensions. The model consists of N particles undergoing dyadic branching Brownian motion with rate 1. At a branching event, the number of particles is kept equal to N by removing the particle located furthest away from the barycenter. To prove the invariance principle, a key step is to establish Harris recurrence for the process viewed from its barycenter.
