2011 Fiscal Year Final Research Report
Advancement of the lace expansion and its applications
| Project/Area Number |
21740059
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hokkaido University |
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Principal Investigator |
SAKAI Akira 北海道大学, 大学院・理学研究院, 准教授 (50506996)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 確率論 |
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| Research Abstract |
The lace expansion has been one of the few mathematically rigorous approaches to investigate critical behavior in high dimensions. We have extended this methodology to obtain a universal sharp asymptotic expression of the 2-point functions for long-range self-avoiding walk and long-range oriented percolation which are defined by power-law decaying pair potentials. We have also investigated the finite-range(but sufficiently spread-out) critical contact process and proved that the n-point function under the Brownian scaling converges to the(n-1)-point function for the canonical measure of super-Brownian motion.
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