Another probabilistic construction of Φ22n

Yichao Huang

doi:10.1214/21-ECP389

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Home > Journals > Electron. Commun. Probab. > Volume 26 > Article

2021 Another probabilistic construction of

{\Phi _{2}^{2n}}

Yichao Huang

Author Affiliations +

Yichao Huang¹
¹Department of Mathematics and Statistics, University of Helsinki

Electron. Commun. Probab. 26: 1-13 (2021). DOI: 10.1214/21-ECP389

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Abstract

This note provides an alternative probabilistic approach to the ${\Phi ^{2n}}$ theory in dimension 2. The key idea is to study the concentration phenomenon of martingales associated to polynomials of Gaussian variables. This is based on an adaptation of the work of Lacoin-Rhodes-Vargas [3] on the quantum Mabuchi K-energy.

Funding Statement

This work was supported by the ERC grant QFPROBA, No.741487.

Acknowledgments

The author is indebted to Christophe Garban, Rémi Rhodes and Vincent Vargas for communicating the idea. We are grateful for the referees’ numerous comments that helped to improve the article.

Citation

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Yichao Huang. "Another probabilistic construction of ${\Phi _{2}^{2n}}$ ." Electron. Commun. Probab. 26 1 - 13, 2021. https://doi.org/10.1214/21-ECP389