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Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs


 
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1. Title Title of document Fluctuations of maxima of discrete Gaussian free fields on a class of recurrent graphs
 
2. Creator Author's name, affiliation, country Takashi Kumagai; RIMS, Kyoto; Japan
 
2. Creator Author's name, affiliation, country Ofer Zeitouni; Weizmann Institute; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian free field; fractal graphs
 
3. Subject Subject classification 60G15; 28A80
 
4. Description Abstract We provide conditions that ensure that the maximum of the Gaussian free field on a sequence of graphs fluctuates at the same order as the field at the point of maximal standard deviation; under these conditions, the expectation of the maximum is of the same order as the maximal standard deviation. In particular, on a sequence of such graphs the recentered maximum is not tight, similarly to the situation in $\mathbb{Z}$ but in contrast with the situation in $\mathbb{Z}^2$. We show that our conditions cover a large class of "fractal" graphs.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-09-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2632
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2632
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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