RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED

Gong, Fu-Zhou; Liu, Yuan; Wen, Zhi-Ying

doi:info:doi/10.18910/25089

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タイトル	RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED
著者	Gong, Fu-Zhou Gong, Fu-Zhou
	Liu, Yuan Liu, Yuan
	Wen, Zhi-Ying Wen, Zhi-Ying
抄録	Recently, Y. Ollivier defined the Ricci curvature of Markov chains on Polish spaces via the contractivity of transition kernels under the L^1 Wasserstein metric. In this paper, we will discuss further the spectral gap, entropy decay, and logarithmic Sobolev inequality for the λ-range gradient operator. As an application, given resistance forms (i.e. symmetric Dirichlet forms with finite effective resistance) on fractals, we can construct Markov chains with positive Ricci curvature, which yields the Gaussian-then-exponential concentration of invariant distributions for Lipschitz test functions.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	50
号	2
開始ページ	491
終了ページ	502
刊行年月	2013-06
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/25089
言語	英語
DOI	info:doi/10.18910/25089
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 2　(2013-6）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.50(2) P.491-P.502
DC.title	RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED
DC.creator	Gong, Fu-Zhou
	Liu, Yuan
	Wen, Zhi-Ying
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2013-06
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/25089
DCTERMS.abstract	Recently, Y. Ollivier defined the Ricci curvature of Markov chains on Polish spaces via the contractivity of transition kernels under the L^1 Wasserstein metric. In this paper, we will discuss further the spectral gap, entropy decay, and logarithmic Sobolev inequality for the λ-range gradient operator. As an application, given resistance forms (i.e. symmetric Dirichlet forms with finite effective resistance) on fractals, we can construct Markov chains with positive Ricci curvature, which yields the Gaussian-then-exponential concentration of invariant distributions for Lipschitz test functions.
DC.identifier	info:doi/10.18910/25089
citation_title	RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED
citation_author	Gong, Fu-Zhou
	Liu, Yuan
	Wen, Zhi-Ying
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-06
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	2
citation_firstpage	491
citation_lastpage	502
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/25089
citation_doi	info:doi/10.18910/25089

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