RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED

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

doi:https://doi.org/10.18910/25089

RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED

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

Osaka Journal of Mathematics, 2013, 50(2), 491-502

アクセス数:361件（2025-07-09 23:01 集計）

固定URL: https://doi.org/10.18910/25089

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タイトル	RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED
著者	著者名 Gong, Fu-Zhou
	著者名 Liu, Yuan
	著者名 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.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	50(2)
ページ	491-502
刊行年月	2013-06
言語	英語
ハンドルURL	https://hdl.handle.net/11094/25089
DOI	https://doi.org/10.18910/25089
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
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）

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. 2013, 50(2), p. 491-502
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
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2013-06
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	10.18910/25089
DC.format	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_public_url	https://hdl.handle.net/11094/25089
citation_doi_detail	10.18910/25089
citation_doi	https://doi.org/10.18910/25089

RICCI CURVATURE OF MARKOV CHAINS ON POLISH SPACES REVISITED

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