Abstract
We investigate random interlacements on with , and derive the large deviation rate for the probability that the capacity of the interlacement set in a macroscopic box is much smaller than that of the box. As an application, we obtain the large deviation rate for the probability that two independent interlacements have empty intersections in a macroscopic box. Additionally, we prove that conditioning on this event, one of the interlacements will be sparse in terms of capacity within the box. This result is an example of the entropic repulsion phenomenon for random interlacements.
Funding Statement
The first author is supported by the National Key R&D Program of China (No. 2021YFA1002700 and No. 2020YFA0712900) and NSFC (No. 12071012). The second author is partially supported by NSF grant DMS-1953848.
Acknowledgments
The authors would like to thank Bruno Schapira and Jiajun Tong for inspiring discussions and thank Yu Liu and the anonymous referees for their helpful and detailed comments on an earlier version of the manuscript, which substantially improved the exposition of this paper. A large part of this work was done when the second author was an undergraduate at Peking University.
Citation
Xinyi Li. Zijie Zhuang. "On large deviations and intersection of random interlacements." Bernoulli 30 (3) 2102 - 2126, August 2024. https://doi.org/10.3150/23-BEJ1666
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