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Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential

Publication ,  Journal Article
Cooke, B; Herzog, DP; Mattingly, JC; Mckinle, SA; Schmidler, SC
Published in: Communications in Mathematical Sciences
January 1, 2017

We establish ergodicity of the Langevin dynamics for a simple two-particle system involving a Lennard-Jones type potential. Moreover, we show that the dynamics is geometrically ergodic; that is, the system converges to stationarity exponentially fast. Methods from stochastic averaging are used to establish the existence of the appropriate Lyapunov function.

Duke Scholars

Published In

Communications in Mathematical Sciences

DOI

EISSN

1945-0796

ISSN

1539-6746

Publication Date

January 1, 2017

Volume

15

Issue

7

Start / End Page

1987 / 2025

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Cooke, B., Herzog, D. P., Mattingly, J. C., Mckinle, S. A., & Schmidler, S. C. (2017). Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential. Communications in Mathematical Sciences, 15(7), 1987–2025. https://doi.org/10.4310/CMS.2017.v15.n7.a10
Cooke, B., D. P. Herzog, J. C. Mattingly, S. A. Mckinle, and S. C. Schmidler. “Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential.” Communications in Mathematical Sciences 15, no. 7 (January 1, 2017): 1987–2025. https://doi.org/10.4310/CMS.2017.v15.n7.a10.
Cooke B, Herzog DP, Mattingly JC, Mckinle SA, Schmidler SC. Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential. Communications in Mathematical Sciences. 2017 Jan 1;15(7):1987–2025.
Cooke, B., et al. “Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential.” Communications in Mathematical Sciences, vol. 15, no. 7, Jan. 2017, pp. 1987–2025. Scopus, doi:10.4310/CMS.2017.v15.n7.a10.
Cooke B, Herzog DP, Mattingly JC, Mckinle SA, Schmidler SC. Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential. Communications in Mathematical Sciences. 2017 Jan 1;15(7):1987–2025.

Published In

Communications in Mathematical Sciences

DOI

EISSN

1945-0796

ISSN

1539-6746

Publication Date

January 1, 2017

Volume

15

Issue

7

Start / End Page

1987 / 2025

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics