8 papers
Uniformity of extremal behaviour along geodesics in Liouville quantum gravity
Manan Bhatia, Konstantinos Kavvadias
In random geometry, geodesics often have a tendency to coalesce together and traverse regions highly singular relative to typical environments. In this paper, working with the mode…
Regularity of the SLE uniformizing map and the SLE trace
Konstantinos Kavvadias, Jason Miller, Lukas Schoug
We show that the modulus of continuity of the SLE uniformizing map is given by as . As a consequence of our analysis, we show that the Jon…
Conformal removability of non-simple Schramm-Loewner evolutions
Konstantinos Kavvadias, Jason Miller, Lukas Schoug
We consider the Schramm-Loewner evolution (SLE) for , which is the regime that the curve is self-intersecting but not space-filling. We let be the…
Two-sided heat kernel bounds for -Liouville Brownian motion
Sebastian Andres, Naotaka Kajino, Konstantinos Kavvadias +1
Liouville Brownian motion (LBM) is the canonical diffusion process on a Liouville quantum gravity (LQG) surface. In this work, we establish upper and lower bounds for the heat kern…
Strong confluence of geodesics in Liouville quantum gravity
Manan Bhatia, Konstantinos Kavvadias
-Liouville quantum gravity (-LQG) constitutes a family of planar random geometries whose geodesics exhibit intricate fractal behaviour. As is observed in various planar model…
Continuity in and tightness of the LQG metric
Konstantinos Kavvadias
We show that the law of the -LQG metric (appropriately renormalized) is continuous in with respect to the local uniform topology of metrics on $\mathbf{C} \times…