{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:30:29Z","timestamp":1762299029053},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:00:00Z","timestamp":1559260800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:00:00Z","timestamp":1559260800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Potential Anal"],"published-print":{"date-parts":[[2020,8]]},"DOI":"10.1007\/s11118-019-09786-8","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T08:02:35Z","timestamp":1559289755000},"page":"727-771","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Two-Dimensional Brownian Random Interlacements"],"prefix":"10.1007","volume":"53","author":[{"given":"Francis","family":"Comets","sequence":"first","affiliation":[]},{"given":"Serguei","family":"Popov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,5,31]]},"reference":[{"key":"9786_CR1","unstructured":"Abe, Y.: Second order term of cover time for planar simple random walk arXiv:\n                  1709.08151\n                  \n                 (2017)"},{"issue":"1","key":"9786_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11134-006-9001-x","volume":"55","author":"F Baccelli","year":"2007","unstructured":"Baccelli, F., Kim, K.B., McDonald, D.: Equilibria of a class of transport equations arising in congestion control. Queueing Syst. 55(1), 1\u20138 (2007)","journal-title":"Queueing Syst."},{"key":"9786_CR3","doi-asserted-by":"crossref","unstructured":"Baccelli, F., Carofiglio, G., Piancino, M.: Stochastic analysis of scalable TCP. In: Proceedings IEEE INFOCOM 2009, pp 19\u201327 (2009)","DOI":"10.1109\/INFCOM.2009.5061902"},{"issue":"1","key":"9786_CR4","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s00440-015-0689-6","volume":"167","author":"D Belius","year":"2017","unstructured":"Belius, D., Kistler, N.: The subleading order of two dimensional cover times. Probab. Theory Relat. Fields 167(1), 461\u2013552 (2017)","journal-title":"Probab. Theory Relat. Fields"},{"key":"9786_CR5","unstructured":"Belius, D., Rosen, J., Zeitouni, O.: Tightness for the cover time of compact two dimensional manifolds. arXiv:\n                  1711.02845\n                  \n                 (2017)"},{"key":"9786_CR6","doi-asserted-by":"publisher","first-page":"2750","DOI":"10.1016\/j.spa.2017.10.001","volume":"128","author":"D Camargo","year":"2018","unstructured":"Camargo, D., Popov, S.: One-dimensional random interlacements. Stochastic Process. Appl. 128, 2750\u20132778 (2018)","journal-title":"Stochastic Process. Appl."},{"key":"9786_CR7","doi-asserted-by":"publisher","DOI":"10.1090\/clrm\/035","volume-title":"Excursions in Classical Analysis","author":"H Chen","year":"2010","unstructured":"Chen, H.: Excursions in Classical Analysis. Mathematical Association of America, Washington, DC (2010)"},{"key":"9786_CR8","doi-asserted-by":"publisher","first-page":"2005","DOI":"10.1007\/s00023-014-0375-8","volume":"16","author":"R Chetrite","year":"2015","unstructured":"Chetrite, R., Touchette, H.: Nonequilibrium Markov processes conditioned on large deviations. Ann. Inst. Henri Poincar\u00e9 B Probab. Stat. 16, 2005\u20132057 (2015)","journal-title":"Ann. Inst. Henri Poincar\u00e9 B Probab. Stat."},{"key":"9786_CR9","volume-title":"From random walk trajectories to random interlacements. Ensaios Matem\u00e1ticos [Mathematical Surveys], vol. 23","author":"J \u010cern\u00fd","year":"2012","unstructured":"\u010cern\u00fd, J., Teixeira, A.: From random walk trajectories to random interlacements. Ensaios Matem\u00e1ticos [Mathematical Surveys], vol. 23. Sociedade Brasileira de Matem\u00e1tica, Rio de Janeiro (2012)"},{"key":"9786_CR10","doi-asserted-by":"publisher","first-page":"4752","DOI":"10.1214\/17-AOP1177","volume":"45","author":"F Comets","year":"2017","unstructured":"Comets, F., Popov, S.: The vacant set of two-dimensional critical random interlacement is infinite. Ann. Probab. 45, 4752\u20134785 (2017)","journal-title":"Ann. Probab."},{"key":"9786_CR11","first-page":"article 96","volume":"18","author":"F Comets","year":"2013","unstructured":"Comets, F., Gallesco, C., Popov, S., Vachkovskaia, M.: On large deviations for the cover time of two-dimensional torus. Electr. J. Probab. 18, article 96 (2013)","journal-title":"Electr. J. Probab."},{"key":"9786_CR12","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s00220-015-2531-5","volume":"343","author":"F Comets","year":"2016","unstructured":"Comets, F., Popov, S., Vachkovskaia, M.: Two-dimensional random interlacements and late points for random walks. Commun. Math. Phys. 343, 129\u2013164 (2016)","journal-title":"Commun. Math. Phys."},{"key":"9786_CR13","doi-asserted-by":"publisher","first-page":"3221","DOI":"10.1016\/j.spa.2017.10.015","volume":"128","author":"DF de Bernardini","year":"2018","unstructured":"de Bernardini, D.F., Gallesco, C.F., Popov, S.: On uniform closeness of local times of Markov chains and i.i.d. sequences. Stochastic Process. Appl. 128, 3221\u20133252 (2018)","journal-title":"Stochastic Process. Appl."},{"issue":"2","key":"9786_CR14","doi-asserted-by":"publisher","first-page":"433","DOI":"10.4007\/annals.2004.160.433","volume":"160","author":"A Dembo","year":"2004","unstructured":"Dembo, A., Peres, Y., Rosen, J., Zeitouni, O.: Cover times for Brownian motion and random walks in two dimensions. Ann. Math. (2) 160(2), 433\u2013464 (2004)","journal-title":"Ann. Math. (2)"},{"issue":"1","key":"9786_CR15","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1214\/009117905000000387","volume":"34","author":"A Dembo","year":"2006","unstructured":"Dembo, A., Peres, Y., Rosen, J., Zeitouni, O.: Late points for random walks in two dimensions. Ann. Probab. 34(1), 219\u2013263 (2006)","journal-title":"Ann. Probab."},{"key":"9786_CR16","unstructured":"Dereich, S., D\u00f6ring, L.: Random interlacements via Kuznetsov measures. arXiv:\n                  1501.00649\n                  \n                 (2015)"},{"key":"9786_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5208-5","volume-title":"Classical Potential Theory and Its Probabilistic Counterpart","author":"JL Doob","year":"1984","unstructured":"Doob, JL: Classical Potential Theory and Its Probabilistic Counterpart. Springer, Berlin (1984)"},{"key":"9786_CR18","doi-asserted-by":"publisher","first-page":"431","DOI":"10.24033\/bsmf.1494","volume":"85","author":"JL Doob","year":"1957","unstructured":"Doob, J. L.: Conditional Brownian motion and the boundary limits of harmonic functions. Bull. Soc. Math. France 85, 431\u2013458 (1957)","journal-title":"Bull. Soc. Math. France"},{"key":"9786_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-05852-8","volume-title":"An Introduction to Random Interlacements","author":"A Drewitz","year":"2014","unstructured":"Drewitz, A., R\u00e1th, B., Sapozhnikov, A.: An Introduction to Random Interlacements. Springer, Berlin (2014)"},{"issue":"1\u20132","key":"9786_CR20","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s00440-013-0525-9","volume":"160","author":"J Goodman","year":"2014","unstructured":"Goodman, J., den Hollander, F.: Extremal geometry of a Brownian porous medium. Probab. Theory Relat. Fields 160(1\u20132), 127\u2013174 (2014)","journal-title":"Probab. Theory Relat. Fields"},{"key":"9786_CR21","volume-title":"Limit Theorems for Stochatic Processes. Grundlehren der mathematischen Wissenschaften","author":"J Jacod","year":"2003","unstructured":"Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochatic Processes. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (2003)"},{"key":"9786_CR22","volume-title":"Poisson Processes","author":"JFC Kingman","year":"1993","unstructured":"Kingman, J.F.C.: Poisson Processes. Oxford University Press, New York (1993)"},{"key":"9786_CR23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511750854","volume-title":"Random walk: a modern introduction. Cambridge Studies in Advanced Mathematics, 123","author":"G Lawler","year":"2010","unstructured":"Lawler, G., Limic, V.: Random walk: a modern introduction. Cambridge Studies in Advanced Mathematics, 123. Cambridge University Press, Cambridge (2010)"},{"issue":"4","key":"9786_CR24","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1007\/s00440-003-0319-6","volume":"128","author":"GF Lawler","year":"2004","unstructured":"Lawler, G.F., Werner, W.: The Brownian loop soup. Probab. Theory Relat. Fields 128(4), 565\u2013588 (2004)","journal-title":"Probab. Theory Relat. Fields"},{"issue":"4","key":"9786_CR25","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1090\/S0894-0347-03-00430-2","volume":"16","author":"GF Lawler","year":"2003","unstructured":"Lawler, G.F., Schramm, O., Werner, W.: Conformal restriction: the chordal case. J. Am. Math. Soc. 16(4), 917\u2013955 (2003)","journal-title":"J. Am. Math. Soc."},{"key":"9786_CR26","first-page":"111","volume-title":"Some properties of planar Brownian motion. Ecole d\u2019\u00c9t\u00e9 de Probabilit\u00e9s de Saint-Flour X\u20131990. Lecture Notes in Math., 1527","author":"JF Le Gall","year":"1992","unstructured":"Le Gall, J.F.: Some properties of planar Brownian motion. Ecole d\u2019\u00c9t\u00e9 de Probabilit\u00e9s de Saint-Flour X\u20131990. Lecture Notes in Math., 1527, pp 111\u2013235. Springer, Berlin (1992)"},{"key":"9786_CR27","volume-title":"Markov Paths, Loops and Fields (Saint-Flour Probability Summer School 2008). Lect. Notes Math. 2026","author":"Y Le Jan","year":"2011","unstructured":"Le Jan, Y: Markov Paths, Loops and Fields (Saint-Flour Probability Summer School 2008). Lect. Notes Math. 2026. Springer, Berlin (2011)"},{"key":"9786_CR28","unstructured":"Li, X.: Percolative properties of Brownian interlacements and its vacant set. arXiv:\n                  1610.08204\n                  \n                 (2016)"},{"issue":"1\u20132","key":"9786_CR29","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s00440-014-0550-3","volume":"161","author":"X Li","year":"2015","unstructured":"Li, X., Sznitman, A.-S.: Large deviations for occupation time profiles of random interlacements. Probab. Theory Relat. Fields 161(1\u20132), 309\u2013350 (2015)","journal-title":"Probab. Theory Relat. Fields"},{"key":"9786_CR30","volume-title":"Brownian Motion","author":"P M\u00f6rters","year":"2010","unstructured":"M\u00f6rters, P., Peres, Y.: Brownian Motion. Cambridge University Press, Cambridge (2010)"},{"key":"9786_CR31","doi-asserted-by":"crossref","unstructured":"Pitman, J., Yor, M.: Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. In: Ikeda, N., Watanabe, S., Fukushima, M., Kunita, H. (eds.) It\u00f4\u2019s Stochastic Calculus and Probability Theory. Springer, Berlin (1996)","DOI":"10.1007\/978-4-431-68532-6_19"},{"issue":"10","key":"9786_CR32","doi-asserted-by":"publisher","first-page":"2545","DOI":"10.4171\/JEMS\/565","volume":"17","author":"S Popov","year":"2015","unstructured":"Popov, S., Teixeira, A.: Soft local times and decoupling of random interlacements. J. Eur. Math. Soc. 17(10), 2545\u20132593 (2015)","journal-title":"J. Eur. Math. Soc."},{"key":"9786_CR33","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623776","volume-title":"Potential Theory in the Complex Plane","author":"T Ransford","year":"1995","unstructured":"Ransford, T.: Potential Theory in the Complex Plane. Cambridge University Press, Cambridge (1995)"},{"key":"9786_CR34","unstructured":"Rodriguez, P.-F.: On pinned fields, interlacements, and random walk on $(\\mathbb {Z}\/N\\mathbb {Z})^{2}$. arXiv:\n                  1705.01934\n                  \n                 To appear in: Probab. Theory Relat. Fields (2017)"},{"issue":"5","key":"9786_CR35","doi-asserted-by":"publisher","first-page":"1849","DOI":"10.1016\/j.spa.2014.01.002","volume":"124","author":"J Rosen","year":"2014","unstructured":"Rosen, J.: Intersection local times for interlacements. Stochastic Process. Appl. 124(5), 1849\u20131880 (2014)","journal-title":"Stochastic Process. Appl."},{"key":"9786_CR36","doi-asserted-by":"crossref","unstructured":"Roynette, B., Yor, M.: Penalising Brownian Paths. Lect. Notes Math. 1969. Springer Science & Business Media (2009)","DOI":"10.1007\/978-3-540-89699-9"},{"issue":"3","key":"9786_CR37","doi-asserted-by":"publisher","first-page":"2039","DOI":"10.4007\/annals.2010.171.2039","volume":"171","author":"A-S Sznitman","year":"2010","unstructured":"Sznitman, A.-S.: Vacant set of random interlacements and percolation. Ann. Math. (2) 171(3), 2039\u20132087 (2010)","journal-title":"Ann. Math. (2)"},{"key":"9786_CR38","doi-asserted-by":"publisher","DOI":"10.4171\/109","volume-title":"Topics in occupation times and Gaussian free fields. Zurich Lect. Adv. Math.","author":"A-S Sznitman","year":"2012","unstructured":"Sznitman, A.-S.: Topics in occupation times and Gaussian free fields. Zurich Lect. Adv. Math. European Mathematical Society, Z\u00fcrich (2012)"},{"issue":"4","key":"9786_CR39","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1007\/s00574-013-0025-7","volume":"44","author":"AS Sznitman","year":"2013","unstructured":"Sznitman, A.S.: On scaling limits and Brownian interlacements. Bull. Braz. Math. Soc. (N.S.) 44(4), 555\u2013592 (2013)","journal-title":"Bull. Braz. Math. Soc. (N.S.)"},{"key":"9786_CR40","doi-asserted-by":"publisher","first-page":"1604","DOI":"10.1214\/EJP.v14-670","volume":"14","author":"A Teixeira","year":"2009","unstructured":"Teixeira, A.: Interlacement percolation on transient weighted graphs. Electr. J. Probab. 14, 1604\u20131627 (2009)","journal-title":"Electr. J. Probab."},{"issue":"3","key":"9786_CR41","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/BF01192257","volume":"98","author":"W Werner","year":"1994","unstructured":"Werner, W.: Sur la forme des composantes connexes du compl\u00e9mentaire de la courbe brownienne plane. Probab. Theory Relat. Fields 98(3), 307\u2013337 (1994)","journal-title":"Probab. Theory Relat. Fields"},{"issue":"3","key":"9786_CR42","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1112\/plms\/s3-28.4.738","volume":"28","author":"D Williams","year":"1974","unstructured":"Williams, D.: Path decomposition and continuity of local time for one-dimensional diffusions. I. Proc. London Math. Soc. 28(3), 738\u2013768 (1974)","journal-title":"Proc. London Math. Soc."},{"key":"9786_CR43","doi-asserted-by":"crossref","unstructured":"Wu, H.: On the occupation times of Brownian excursions and Brownian loops. S\u00e9minaire de Probabilit\u00e9s XLIV (Lect. Notes Math. 2046), pp. 149\u2013166 (2012)","DOI":"10.1007\/978-3-642-27461-9_7"}],"container-title":["Potential Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11118-019-09786-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11118-019-09786-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11118-019-09786-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,18]],"date-time":"2020-07-18T02:03:26Z","timestamp":1595037806000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11118-019-09786-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,31]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["9786"],"URL":"https:\/\/doi.org\/10.1007\/s11118-019-09786-8","relation":{},"ISSN":["0926-2601","1572-929X"],"issn-type":[{"value":"0926-2601","type":"print"},{"value":"1572-929X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,31]]},"assertion":[{"value":"23 July 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 May 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}