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- W3203863159 abstract "We show that for each ${mathbf c}_{mathrm M} in [1,25)$, there is a unique metric associated with Liouville quantum gravity (LQG) with matter central charge ${mathbf c}_{mathrm M}$. An earlier series of works by Ding-Dub'edat-Dunlap-Falconet, Gwynne-Miller, and others showed that such a metric exists and is unique in the subcritical case ${mathbf c}_{mathrm M} in (-infty,1)$, which corresponds to coupling constant $gamma in (0,2)$. The critical case ${mathbf c}_{mathrm M} = 1$ corresponds to $gamma=2$ and the supercritical case ${mathbf c}_{mathrm M} in (1,25)$ corresponds to $gamma in mathbb C$ with $|gamma| = 2$. Our metric is constructed as the limit of an approximation procedure called Liouville first passage percolation, which was previously shown to be tight for $mathbf c_{mathrm M} in [1,25)$ by Ding and Gwynne (2020). In this paper, we show that the subsequential limit is uniquely characterized by a natural list of axioms. This extends the characterization of the LQG metric proven by Gwynne and Miller (2019) for $mathbf c_{mathrm M} in (-infty,1)$ to the full parameter range $mathbf c_{mathrm M} in (-infty,25)$. Our argument is substantially different from the proof of the characterization of the LQG metric for $mathbf c_{mathrm M} in (-infty,1)$. In particular, the core part of the argument is simpler and does not use confluence of geodesics." @default.
- W3203863159 created "2021-10-11" @default.
- W3203863159 creator A5035621341 @default.
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- W3203863159 date "2021-09-30" @default.
- W3203863159 modified "2023-09-26" @default.
- W3203863159 title "Uniqueness of the critical and supercritical Liouville quantum gravity metrics" @default.
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- W3203863159 doi "https://doi.org/10.48550/arxiv.2110.00177" @default.
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