On the spectral gap of the kac walk and other binary collision processes on d-dimensional lattice

Makiko Sasada

研究成果: Conference contribution

2 被引用数 (Scopus)

抄録

We give a lower bound on the spectral gap for a class of binary collision processes. In ALEA Lat. Am. J. Probab. Math. Stat. 4, 205-222 (2008), Caputo showed that, for a class of binary collision processes given by simple averages on the complete graph, the analysis of the spectral gap of an N-component system is reduced to that of the same system for N = 3. In this paper, we give a comparison technique to reduce the analysis of the spectral gap of binary collision processes given by simple averages on d-dimensional lattice to that on the complete graph. We also give a comparison technique to reduce the analysis of the spectral gap of binary collision processes which are not given by simple averages to that given by simple averages. Combining them with Caputo's result, we give a new and elementary method to obtain spectral gap estimates. The method applies to a number of binary collision processes on the complete graph and also on d-dimensional lattice, including a class of energy exchange models which was recently introduced in arXiv:1109.2356, and zero-range processes.

本文言語English
ホスト出版物のタイトルSymmetries, Integrable Systems and Representations
出版社Springer New York LLC
ページ543-560
ページ数18
ISBN(印刷版)9781447148623
DOI
出版ステータスPublished - 2013 1 1

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
40
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

ASJC Scopus subject areas

  • Mathematics(all)

フィンガープリント 「On the spectral gap of the kac walk and other binary collision processes on d-dimensional lattice」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル