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Patrik L Ferrari - One of the best experts on this subject based on the ideXlab platform.

  • free energy fluctuations for directed polymers in random media in 1 1 dimension
    Communications on Pure and Applied Mathematics, 2014
    Co-Authors: Alexei Borodin, Ivan Corwin, Patrik L Ferrari
    Abstract:

    We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant Formulas for the Laplace Transform of their partition functions. In particular, we show that for large time τ, the probability distributions for the free energy fluctuations, when rescaled by τ1/3, converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semidiscrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik–Ben Arous–Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm—the Kardar-Parisi-Zhang equation. The Laplace Transform Formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data. © 2014 Wiley Periodicals, Inc.

  • free energy fluctuations for directed polymers in random media in 1 1 dimension
    arXiv: Probability, 2012
    Co-Authors: Alexei Borodin, Ivan Corwin, Patrik L Ferrari
    Abstract:

    We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant Formulas for the Laplace Transform of their partition functions. In particular, we show that for large time tau, the probability distributions for the free energy fluctuations, when rescaled by tau^{1/3}, converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semi-discrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik-Ben Arous-Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm -- the Kardar-Parisi-Zhang equation. The Laplace Transform Formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data.

Alexei Borodin - One of the best experts on this subject based on the ideXlab platform.

  • free energy fluctuations for directed polymers in random media in 1 1 dimension
    Communications on Pure and Applied Mathematics, 2014
    Co-Authors: Alexei Borodin, Ivan Corwin, Patrik L Ferrari
    Abstract:

    We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant Formulas for the Laplace Transform of their partition functions. In particular, we show that for large time τ, the probability distributions for the free energy fluctuations, when rescaled by τ1/3, converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semidiscrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik–Ben Arous–Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm—the Kardar-Parisi-Zhang equation. The Laplace Transform Formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data. © 2014 Wiley Periodicals, Inc.

  • free energy fluctuations for directed polymers in random media in 1 1 dimension
    arXiv: Probability, 2012
    Co-Authors: Alexei Borodin, Ivan Corwin, Patrik L Ferrari
    Abstract:

    We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant Formulas for the Laplace Transform of their partition functions. In particular, we show that for large time tau, the probability distributions for the free energy fluctuations, when rescaled by tau^{1/3}, converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semi-discrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik-Ben Arous-Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm -- the Kardar-Parisi-Zhang equation. The Laplace Transform Formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data.

Ivan Corwin - One of the best experts on this subject based on the ideXlab platform.

  • free energy fluctuations for directed polymers in random media in 1 1 dimension
    Communications on Pure and Applied Mathematics, 2014
    Co-Authors: Alexei Borodin, Ivan Corwin, Patrik L Ferrari
    Abstract:

    We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant Formulas for the Laplace Transform of their partition functions. In particular, we show that for large time τ, the probability distributions for the free energy fluctuations, when rescaled by τ1/3, converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semidiscrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik–Ben Arous–Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm—the Kardar-Parisi-Zhang equation. The Laplace Transform Formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data. © 2014 Wiley Periodicals, Inc.

  • free energy fluctuations for directed polymers in random media in 1 1 dimension
    arXiv: Probability, 2012
    Co-Authors: Alexei Borodin, Ivan Corwin, Patrik L Ferrari
    Abstract:

    We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant Formulas for the Laplace Transform of their partition functions. In particular, we show that for large time tau, the probability distributions for the free energy fluctuations, when rescaled by tau^{1/3}, converges to the GUE Tracy-Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semi-discrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik-Ben Arous-Peche distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm -- the Kardar-Parisi-Zhang equation. The Laplace Transform Formula we prove can be inverted to give the one-point probability distribution of the solution to these stochastic PDEs for the class of initial data.

Shen Jin-fei - One of the best experts on this subject based on the ideXlab platform.

  • Wave Variable Method for Multi-DOF Teleoperation System Control
    Information & Computation, 2012
    Co-Authors: Shen Jin-fei
    Abstract:

    To apply the wave variable method to multi-DOF(degree of freedom) teleoperation system,a more universal wave Transform Formula suitable for multi-DOF teleoperation system is proposed,and the principle of choosing parameters of the Formula is extended.The theory of the wave variable method is analyzed,and the wave Transform Formula for multiDOF system is obtained by replacing the wave impedance constant b with wave impedance matrix.From the energy point of view,the selection principle of wave impedance matrix is analyzed,and then the choosing method and the constraint relation of the impedance matrixes are extended based on the selection principle.The passivity of the extended wave impedance matrix is analyzed based on the scattering theory.Taking a 3-DOF master-slave teleoperation system as example,simulation experiments and teleoperation experiments are conducted,and the experimental results show that the proposed wave Transform Formula can ensure the stability of the multi-DOF teleoperation system with time delays.

Xiaoming Yuan - One of the best experts on this subject based on the ideXlab platform.

  • A whole-space Transform Formula of cylindrical wave functions for scattering problems
    Earthquake Engineering and Engineering Vibration, 2014
    Co-Authors: Xiaoming Yuan
    Abstract:

    The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion, and the wave function expansion technique has been widely used in many subjects. To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters, a whole-space Transform Formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study. The Transforms of wave functions in cylindrical coordinates can be classified into two basic types: interior Transform and exterior Transform, and the existing Graf’s addition theorem is only suitable for the former. By performing a new replacement between the two coordinates, the exterior Transform Formula is first deduced. It is then combined with Graf’s addition theorem to establish a whole-space Transform Formula. By using the whole-space Transform Formula, the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application. The effectiveness and advantages of the whole-space Transform Formula is illustrated by comparison with the approximate model based on a large cycle method. The whole-space Transform Formula presented herein can be used to perform the Transform between two different cylindrical coordinates in the whole space. In addition, its concept and principle are universal and can be further extended to establish the coordinate Transform Formula of wave functions in other coordinate systems.