@article{TEXTUAL,
      recid = {5037},
      author = {Ding, Jian and Gwynne, Ewain},
      title = {Uniqueness of the critical and supercritical Liouville  quantum gravity metrics},
      journal = {Proceedings of the London Mathematical Society},
      address = {2022-11-10},
      number = {TEXTUAL},
      abstract = {We show that for each c<sub>M</sub> ∈ [ 1 , 25 ) ${\mathbf  {c}}_{\mathrm{M}} \in [1,25)$ , there is a unique metric  associated with Liouville quantum gravity (LQG) with matter  central charge c<sub>M</sub> ${\mathbf {c}}_{\mathrm{M}}$ .  An earlier series of works by Ding–Dubédat–Dunlap–Falconet,  Gwynne–Miller, and others showed that such a metric exists  and is unique in the subcritical case c<sub>M</sub> ∈ ( − ∞  , 1 ) ${\mathbf {c}}_{\mathrm{M}} \in (-\infty ,1)$ , which  corresponds to coupling constant γ ∈ ( 0 , 2 ) $\gamma \in  (0,2)$ . The critical case c<sub>M</sub> = 1 ${\mathbf  {c}}_{\mathrm{M}} = 1$ corresponds to γ = 2 $\gamma =2$ and  the supercritical case c<sub>M</sub> ∈ ( 1 , 25 ) ${\mathbf  {c}}_{\mathrm{M}} \in (1,25)$ corresponds to γ ∈ C $\gamma  \in \mathbb {C}$ with | γ | = 2 $|\gamma | = 2$ . Our  metric is constructed as the limit of an approximation  procedure called Liouville first passage percolation, which  was previously shown to be tight for c<sub>M</sub> ∈ [ 1 ,  25 ) $\mathbf {c}_{\mathrm{M}} \in [1,25)$ 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  c<sub>M</sub> ∈ ( − ∞ , 1 ) $\mathbf {c}_{\mathrm{M}} \in  (-\infty ,1)$ to the full parameter range c<sub>M</sub> ∈ (  − ∞ , 25 ) $\mathbf {c}_{\mathrm{M}} \in (-\infty ,25)$ .  Our argument is substantially different from the proof of  the characterization of the LQG metric for c<sub>M</sub> ∈  ( − ∞ , 1 ) $\mathbf {c}_{\mathrm{M}} \in (-\infty ,1)$ .  In particular, the core part of the argument is simpler and  does not use confluence of geodesics.},
      url = {http://knowledge.uchicago.edu/record/5037},
}