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High points for the membrane model in the critical dimension


 
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1. Title Title of document High points for the membrane model in the critical dimension
 
2. Creator Author's name, affiliation, country Alessandra Cipriani; University of Zurich; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Membrane Model;extrema of Gaussian fields;bilaplacian;multiscale decomposition;Hausdorff dimension
 
3. Subject Subject classification 60K35;60G15;60G60
 
4. Description Abstract In this notice we study the fractal structure of the set of high points for the membrane model in the critical dimension $d=4$. We are able to compute the Hausdorff dimension of the set of points which are atypically high, and also that of clusters, showing that high points tend not to be evenly spread on the lattice. We will see that these results follow closely those obtained by O. Daviaud for the 2-dimensional discrete Gaussian Free Field.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Swiss National Science Foundation, grant 138141, and Forschungskredit of the University of Zurich
 
7. Date (YYYY-MM-DD) 2013-09-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2750
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2750
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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