### Abstract

In this paper, we give a simple proof of log-Sobolev inequalities on an infinite volume path space C(ℝ, ℝ^{d}) with Gibbs measures. We introduce a parabolic stochastic partial differential equation which is reversible with respect to the Gibbs measures. In the proof, the gradient estimate for the diffusion semigroup which is derived from the stochastic flow plays a central role.

Original language | English |
---|---|

Pages (from-to) | 321-329 |

Number of pages | 9 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 9 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 Jun 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Gibbs measure
- Gradient estimate
- Log-Sobolev inequality
- SPDE

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Statistics and Probability
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**A simple proof of log-Sobolev inequalities on a path space with Gibbs measures.** / Kawabi, Hiroshi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A simple proof of log-Sobolev inequalities on a path space with Gibbs measures

AU - Kawabi, Hiroshi

PY - 2006/6/1

Y1 - 2006/6/1

N2 - In this paper, we give a simple proof of log-Sobolev inequalities on an infinite volume path space C(ℝ, ℝd) with Gibbs measures. We introduce a parabolic stochastic partial differential equation which is reversible with respect to the Gibbs measures. In the proof, the gradient estimate for the diffusion semigroup which is derived from the stochastic flow plays a central role.

AB - In this paper, we give a simple proof of log-Sobolev inequalities on an infinite volume path space C(ℝ, ℝd) with Gibbs measures. We introduce a parabolic stochastic partial differential equation which is reversible with respect to the Gibbs measures. In the proof, the gradient estimate for the diffusion semigroup which is derived from the stochastic flow plays a central role.

KW - Gibbs measure

KW - Gradient estimate

KW - Log-Sobolev inequality

KW - SPDE

UR - http://www.scopus.com/inward/record.url?scp=33745038536&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745038536&partnerID=8YFLogxK

U2 - 10.1142/S021902570600238X

DO - 10.1142/S021902570600238X

M3 - Article

AN - SCOPUS:33745038536

VL - 9

SP - 321

EP - 329

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

SN - 0219-0257

IS - 2

ER -