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

Makiko Sasada

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationSpringer Proceedings in Mathematics and Statistics
PublisherSpringer New York LLC
Pages543-560
Number of pages18
Volume40
ISBN (Print)9781447148623
DOIs
Publication statusPublished - 2013

Fingerprint

Spectral Gap
Walk
Collision
Binary
Complete Graph
Zero-range Process
Lower bound
Energy
Estimate
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sasada, M. (2013). On the spectral gap of the kac walk and other binary collision processes on d-dimensional lattice. In Springer Proceedings in Mathematics and Statistics (Vol. 40, pp. 543-560). Springer New York LLC. https://doi.org/10.1007/978-1-4471-4863-0_23

On the spectral gap of the kac walk and other binary collision processes on d-dimensional lattice. / Sasada, Makiko.

Springer Proceedings in Mathematics and Statistics. Vol. 40 Springer New York LLC, 2013. p. 543-560.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sasada, M 2013, On the spectral gap of the kac walk and other binary collision processes on d-dimensional lattice. in Springer Proceedings in Mathematics and Statistics. vol. 40, Springer New York LLC, pp. 543-560. https://doi.org/10.1007/978-1-4471-4863-0_23
Sasada M. On the spectral gap of the kac walk and other binary collision processes on d-dimensional lattice. In Springer Proceedings in Mathematics and Statistics. Vol. 40. Springer New York LLC. 2013. p. 543-560 https://doi.org/10.1007/978-1-4471-4863-0_23
Sasada, Makiko. / On the spectral gap of the kac walk and other binary collision processes on d-dimensional lattice. Springer Proceedings in Mathematics and Statistics. Vol. 40 Springer New York LLC, 2013. pp. 543-560
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