K. Kavvadias

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20222026

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math.PR2026

Convergence of the Subcritical $γ$ -LQG Metric to the Critical 2-LQG Metric as $γ \to 2$

Konstantinos Kavvadias

We show that the $γ$ -LQG metric (appropriately re-normalized) for $γ \in (0, 2)$ converges in law to the critical 2-LQG metric (appropriately re-normalized) with respect to the local…

math.PR2026

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…

math.PR2025

Continuity in $ξ$ and $ξ \to \infty$ tightness of the LQG metric

Konstantinos Kavvadias

We show that the law of the $γ$ -LQG metric (appropriately renormalized) is continuous in $γ \in (0, 2)$ with respect to the local uniform topology of metrics on $\mathbf{C} \times \m…

math.PR2025

Two-sided heat kernel bounds for $8/3$ -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…

math.PR2024

SLE $_{κ} (ρ)$ processes in the light cone regime on Liouville quantum gravity

Konstantinos Kavvadias, Jason Miller

We study the relationship between certain SLE $_{κ} (ρ)$ processes, which are variants of the Schramm-Loewner evolution with parameter $κ$ in which one keeps track of an extra marked p…

math.PR2024

Connectivity of the adjacency graph of complementary components of the SLE fan

Cillian Doherty, Konstantinos Kavvadias, Jason Miller

Suppose that $h$ is an instance of the Gaussian free field (GFF) on a simply connected domain $D \subseteq C$ and $x, y \in \partial D$ are distinct. Fix $κ \in (0, 4)$ and…

Convergence of the Subcritical γ-LQG Metric to the Critical 2-LQG Metric as γ→2

Uniformity of extremal behaviour along geodesics in Liouville quantum gravity

Continuity in ξ and ξ→∞ tightness of the LQG metric

Two-sided heat kernel bounds for 8/3​-Liouville Brownian motion

SLEκ​(ρ) processes in the light cone regime on Liouville quantum gravity

Connectivity of the adjacency graph of complementary components of the SLE fan

Convergence of the Subcritical $γ$ -LQG Metric to the Critical 2-LQG Metric as $γ \to 2$

Continuity in $ξ$ and $ξ \to \infty$ tightness of the LQG metric

Two-sided heat kernel bounds for $8/3$ -Liouville Brownian motion

SLE $_{κ} (ρ)$ processes in the light cone regime on Liouville quantum gravity