3 papers
math.PR2026
Dimension lower bounds in random geometry via Lipschitz functions
Manan Bhatia, Ewain Gwynne, Brin Harper
We prove lower bounds for the Hausdorff dimensions of various natural sets associated with the Liouville quantum gravity (LQG) metric. We prove that the set of 3-star points (i.e.,…
math.PR2024
Area measures and branched polymers in supercritical Liouville quantum gravity
Manan Bhatia, Ewain Gwynne, Jinwoo Sung
We study Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which has background charge and central charge $\mathbf{c}_{\mathrm{L}}…
math.PR2023
The -variation of distance profiles in -Liouville quantum gravity
Manan Bhatia
For Brownian surfaces with boundary and an interior marked point, a natural observable to consider is the distance profile, defined as the process of distances from the marked poin…