{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:35:10Z","timestamp":1787333710736,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2019-05408"],"award-info":[{"award-number":["RGPIN-2019-05408"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010318","name":"University of Manitoba","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010318","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Kemeny's constant is an interesting and useful quantifier describing the global average behavior of a Markov chain. In this article, we examine the sensitivity of Kemeny's constant to perturbations in the transition probabilities. That is, we consider the problem of generating a condition number for Kemeny's constant to give an indication of the size of the change in its value relative to the size of the perturbation. We provide a structured condition number and determine some illuminating upper and lower bounds which connect the conditioning of Kemeny's constant to well-studied condition numbers for the stationary vector of the Markov chain. We also investigate the behavior of this structured condition number for several infinite families of Markov chains.<\/jats:p>","DOI":"10.1137\/19m1240964","type":"journal-article","created":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T14:49:11Z","timestamp":1576594151000},"page":"1555-1578","source":"Crossref","is-referenced-by-count":4,"title":["A Structured Condition Number for Kemeny's Constant"],"prefix":"10.1137","volume":"40","author":[{"given":"Jane","family":"Breen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steve","family":"Kirkland","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,12,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(99)00047-4"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2018.68"},{"key":"atypb3","unstructured":"J. Breen,\n                      Markov Chains under Combinatorial Constraints: Analysis and Synthesis\n                      , Ph.D. thesis, University of Manitoba, Winnipeg, Canada, 2018."},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"S. L. Campbell and C. D. Meyer,\n                      Generalized Inverses of Linear Transformations\n                      , reprint of the 1979 original, Classics Appl. Math. 56, SIAM, Philadelphia, 2009,https:\/\/doi.org\/10.1137\/1.9780898719048.","DOI":"10.1137\/1.9780898719048"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-010-9382-1"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1080\/03081089508818406"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(01)00320-2"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(99)00263-3"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2011.568005"},{"key":"atypb10","first-page":"91","author":"Deuflhard P.","year":"2004","journal-title":"Philadelphia"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.2307\/1427341"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479896313188"},{"key":"atypb13","unstructured":"R. Horn and C. Johnson,\n                      Matrix Analysis\n                      , 2nd ed., Cambridge University Press, Cambridge, UK, 2013."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(82)90218-X"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2006.02.008"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.06.016"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2013.08.037"},{"key":"atypb18","unstructured":"J. G. Kemeny and J. L. Snell,\n                      Finite Markov Chains\n                      , The University Series in Undergraduate Mathematics, D. Van Nostrand, Princeton, NJ, 1960."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989326005X"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479801390947"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.1092"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.13001\/1081-3810.1130"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2010.07.016"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s10587-016-0291-9"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"S. Kirkland and M. Neumann,\n                      Group Inverses of M-Matrices and Their Applications\n                      , CRC Press, Boca Raton, FL, 2013.","DOI":"10.1201\/b13054"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-008-0172-8"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2002.11919905"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/0601031"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479892228900"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/1017044"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.2307\/3212261"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.2307\/1427277"},{"key":"atypb33","first-page":"121","author":"Seneta E.","year":"1991","journal-title":"New York"},{"key":"atypb34","doi-asserted-by":"crossref","unstructured":"E. Seneta,\n                      Non-negative Matrices and Markov Chains\n                      , revised reprint of the second (1981) edition, Springer Ser. Statist., Springer, New York, 2006.","DOI":"10.1007\/0-387-32792-4"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1240964","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:18:39Z","timestamp":1787332719000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1240964"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/19M1240964"],"URL":"https:\/\/doi.org\/10.1137\/19m1240964","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}