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Tightness of Liouville first passage percolation for γ∈(0,2)
Publications Mathématiques de l'IHÉS, Volume 132 (2020), pp. 353-403
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We study Liouville first passage percolation metrics associated to a Gaussian free field h mollified by the two-dimensional heat kernel p t in the bulk, and related star-scale invariant metrics. For γ∈(0,2) and ξ=γ d γ , where d γ is the Liouville quantum gravity dimension defined in Ding and Gwynne (Commun. Math. Phys. 374:1877–1934, 2020), we show that renormalized metrics (λ t -1 e ξp t *h ds) t∈(0,1) are tight with respect to the uniform topology. We also show that subsequential limits are bi-Hölder with respect to the Euclidean metric, obtain tail estimates for side-to-side distances, and derive error bounds for the normalizing constants λ t .

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DOI: 10.1007/s10240-020-00121-1 
@article{PMIHES_2020__132__353_0,
     author = {Jian Ding and Julien Dub\'edat and Alexander Dunlap and Hugo Falconet},
     title = {Tightness of {Liouville} first passage percolation for $\gamma \in (0,2)$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {353--403},
     year = {2020},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {132},
     doi = {10.1007/s10240-020-00121-1},
     language = {en},
     url = {https://pmihes.centre-mersenne.org/articles/10.1007/s10240-020-00121-1/}
}
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Jian Ding; Julien Dubédat; Alexander Dunlap; Hugo Falconet. Tightness of Liouville first passage percolation for $\gamma \in (0,2)$. Publications Mathématiques de l'IHÉS, Volume 132 (2020), pp. 353-403. doi: 10.1007/s10240-020-00121-1

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