The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
A. G. Kachurovskii - One of the best experts on this subject based on the ideXlab platform.
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Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem
Mathematical Notes, 2019Co-Authors: A. G. Kachurovskii, I. V. PodviginAbstract:Estimates of the Rate of Convergence in the Birkhoff ergodic theorem which hold almost everywhere are considered. For the action of an ergodic automorphism, the existence of such estimates is proved, their structure is studied, and unimprovability questions are considered.
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on the constants in the estimates of the Rate of Convergence in von neumann s ergodic theorem
Mathematical Notes, 2010Co-Authors: A. G. Kachurovskii, Vladimir Viktorovich SedalishchevAbstract:We study the Rate of Convergence in von Neumann’s ergodic theorem. We obtain constants connecting the power Rate of Convergence of ergodic means and the power singularity at zero of the spectral measure of the corresponding dynamical system (these concepts are equivalent to each other). All the results of the paper have obvious exact analogs for wide-sense stationary stochastic processes.
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on the Rate of Convergence in von neumann s ergodic theorem with continuous time
Sbornik Mathematics, 2010Co-Authors: A. G. Kachurovskii, Anna Valentinovna ReshetenkoAbstract:The Rate of Convergence in von Neumann's mean ergodic theorem is studied for continuous time. The condition that the Rate of Convergence of the ergodic averages be of power-law type is shown to be equivalent to requiring that the spectral measure of the corresponding dynamical system have a power-type singularity at 0. This forces the estimates for the Convergence Rate in the above ergodic theorem to be necessarily spectral. All the results obtained have obvious exact analogues for wide-sense stationary processes. Bibliography: 7 titles.
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The Rate of Convergence in ergodic theorems
Russian Mathematical Surveys, 1996Co-Authors: A. G. KachurovskiiAbstract:Contents Introduction 0.1. Notation 0.2. On uniform estimates 0.3. Brief description of new results Chapter I. Rate of Convergence in the pointwise ergodic theorem § 1. Growth of the dispersion 1.1. Spectral measures and power-function growth of dispersion 1.2. Proof of Theorem 3 1.3. Correlation coefficients and dispersion growth § 2. Decay of the probability of an e-deviation 2.1. The case of independent 2.2. Decay of and growth of 2.3. On the Rate of approximation of by functions cohomologous to zero 2.4. Proofs of Theorems 11 and 12 § 3. On the law of the iteRated logarithm 3.1. The growth of and the law of the iteRated logarithm § 4. On uniform Convergence 4.1. The fastest uniform Convergence 4.2. Two criteria for weak mixing Chapter II. Oscillation of averages in the pointwise ergodic theorem § 5. Crossings of an interval § 6. e-fluctuations § 7. p-variation Chapter III. Rate of Convergence and oscillations in other ergodic theorems § 8. Rate of Convergence § 9. Oscillations Appendix 1. Interpretation in terms of non-standard analysis A1.1. The theory of internal sets A1.2. Elementary analogues of ergodic theorems Appendix 2. Estimates of large deviations of the random number of fluctuations of averages for independent terms A2.1. Formulation of the basic result A2.2. Outline of the proof of Theorem 33 Appendix 3. Fluctuations of bounded martingales Bibliography
Quansheng Liu - One of the best experts on this subject based on the ideXlab platform.
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Rate of Convergence for polymers in a weak disorder
Journal of Mathematical Analysis and Applications, 2017Co-Authors: Francis Comets, Quansheng LiuAbstract:We consider directed polymers in random environment on the lattice $Z^d$ at small inverse temperature and dimension $d \geq 3$. Then, the normalized partition function $W_n$ is a regular martingale with limit W. We prove that $n^{(d−2)/4} (W_n−W)/W_n $ converges in distribution to a Gaussian law. Both the polynomial Rate of Convergence and the scaling with the martingale $W_n$ are different from those for polymers on trees.
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Rate of Convergence for polymers in a weak disorder
2016Co-Authors: Francis Comets, Quansheng LiuAbstract:We consider directed polymers in random environment on the lattice Z d at small inverse temperature and dimension d ≥ 3. Then, the normalized partition function W n is a regular martingale with limit W. We prove that n (d−2)/4 (W n − W)/W n converges in distribution to a Gaussian law. Both the polynomial Rate of Convergence and the scaling with the martingale W n are different from those for polymers on trees.
Mark Braverman - One of the best experts on this subject based on the ideXlab platform.
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The Rate of Convergence of the Walk on Spheres Algorithm
Geometric and Functional Analysis, 2012Co-Authors: Ilia Binder, Mark BravermanAbstract:In this paper we examine the Rate of Convergence of one of the standard algorithms for emulating exit probabilities of Brownian motion, the Walk on Spheres (WoS) algorithm. We obtain a complete characterization of the Rate of Convergence of WoS in terms of the local geometry of a domain.
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The Rate of Convergence of the Walk on Spheres Algorithm
arXiv: Probability, 2008Co-Authors: Ilia Binder, Mark BravermanAbstract:In this paper we examine the Rate of Convergence of one of the standard algorithms for emulating exit probabilities of Brownian motion, the Walk on Spheres (WoS) algorithm. We obtain the complete characterization of the Rate of Convergence of WoS in terms of the local geomnetry of a domain.
Benjamin Schlein - One of the best experts on this subject based on the ideXlab platform.
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quantum fluctuations and Rate of Convergence towards mean field dynamics
Communications in Mathematical Physics, 2009Co-Authors: Igor Rodnianski, Benjamin SchleinAbstract:The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the Rate of Convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics. More precisely, we prove bounds on the difference between the one-particle density associated with the solution of the N-body Schrodinger equation and the orthogonal projection onto the solution of the Hartree equation.
Timothy G Griffin - One of the best experts on this subject based on the ideXlab platform.
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Rate of Convergence of increasing path vector routing protocols
International Conference on Network Protocols, 2018Co-Authors: Matthew L Daggitt, Timothy G GriffinAbstract:A good measure of the Rate of Convergence of path-vector protocols is the number of synchronous iterations required for Convergence in the worst case. From an algebraic perspective, the Rate of Convergence depends on the expressive power of the routing algebra associated with the protocol. For example in a network of n nodes, shortest-path protocols are guaranteed to converge in O(n) iterations. In contrast the algebra underlying the Border Gateway Protocol (BGP) is in some sense too expressive and the protocol is not guaranteed to converge. There is significant interest in finding well-behaved algebras that still have enough expressive power to satisfy network operators. Recent theoretical results have shown that by constraining routing algebras to those that are "strictly increasing" we can guarantee the Convergence of path-vector protocols. Currently the best theoretical worst-case upper bound for the Convergence of such algebras is O(n!) iterations. However in practice it is difficult to find examples that do not converge in n iterations. In this paper we close this gap. We first present a family of network configurations that converges in Θ(n^2) iterations, demonstrating that the worst case is Ω(n^2) iterations. We then prove that path-vector protocols with a strictly increasing algebra are guaranteed to converge in O(n^2) iterations. Together these results establish a tight Θ(n^2) bound. This is another piece of the puzzle in showing that "strictly increasing" is, at least on a technical level, a reasonable constraint for practical policy-rich protocols.
