K. Kavvadias

activity

20172026

most citedNowhere differentiable functions with respect to the position

3 citations · 3 across the 14 of their papers we have counts for

collaborators

15 papers

math.PR2026

The conformally invariant metric on CLE $_{4}$ III: uniqueness

Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1

This paper is the third and final article in a series of papers constructing the canonical conformally invariant metric on the set of loops of the conformal loop ensemble (CLE) wit…

math.PR2026

The conformally invariant metric on CLE $_{4}$ II: existence of geodesics

Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1

We continue our study of the conformal loop ensemble (CLE) with parameter $κ = 4$ , the critical threshold at or below which the loops are simple and disjoint, touching neither each o…

math.PR2026

The conformally invariant metric on CLE $_{4}$ I: subsequential limits of the non-simple CLE graph metric

Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1

We consider the conformal loop ensemble (CLE) with the parameter $κ = 4$ , the critical value at or below which the loops are simple and do not intersect each other or the domain boun…

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

Strong confluence of geodesics in Liouville quantum gravity

Manan Bhatia, Konstantinos Kavvadias

$γ$ -Liouville quantum gravity ( $γ$ -LQG) constitutes a family of planar random geometries whose geodesics exhibit intricate fractal behaviour. As is observed in various planar model…

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…

math.PR2023

Conformal removability of non-simple Schramm-Loewner evolutions

Konstantinos Kavvadias, Jason Miller, Lukas Schoug

We consider the Schramm-Loewner evolution (SLE $_{κ}$ ) for $κ \in (4, 8)$ , which is the regime that the curve is self-intersecting but not space-filling. We let $K$ be the se…

math.PR2022

Conformal removability of SLE $_{4}$

Konstantinos Kavvadias, Jason Miller, Lukas Schoug

We consider the Schramm-Loewner evolution (SLE $_{κ}$ ) with $κ = 4$ , the critical value of $κ > 0$ at or below which SLE $_{κ}$ is a simple curve and above which it is self-intersecting. We…

math.PR2022

Bipolar oriented random planar maps with large faces and exotic SLE $_{κ} (ρ)$ processes

Konstantinos Kavvadias, Jason Miller

We consider bipolar oriented random planar maps with heavy-tailed face degrees. We show for each $α \in (1, 2)$ that if the face degree is in the domain of attraction of an $α$ -stabl…

math.PR2021

Regularity of the SLE $_{4}$ uniformizing map and the SLE $_{8}$ trace

Konstantinos Kavvadias, Jason Miller, Lukas Schoug

We show that the modulus of continuity of the SLE $_{4}$ uniformizing map is given by $(lo g δ^{- 1})^{- 1/3 + o (1)}$ as $δ \to 0$ . As a consequence of our analysis, we show that the Jones…

math.CV2017★ 3 cited

Nowhere differentiable functions with respect to the position

K. Kavvadias, K. Makridis

Let $Ω$ be a bounded domain in $C$ such that $\partial Ω$ does not contain isolated points. Let $R (Ω)$ be the space of uniform limits on $Ω$ of rational functions…

The conformally invariant metric on CLE4​ III: uniqueness

The conformally invariant metric on CLE4​ II: existence of geodesics

The conformally invariant metric on CLE4​ I: subsequential limits of the non-simple CLE graph metric

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

Strong confluence of 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

Conformal removability of non-simple Schramm-Loewner evolutions

Conformal removability of SLE4​

Bipolar oriented random planar maps with large faces and exotic SLEκ​(ρ) processes

Regularity of the SLE4​ uniformizing map and the SLE8​ trace

Nowhere differentiable functions with respect to the position

The conformally invariant metric on CLE $_{4}$ III: uniqueness

The conformally invariant metric on CLE $_{4}$ II: existence of geodesics

The conformally invariant metric on CLE $_{4}$ I: subsequential limits of the non-simple CLE graph metric

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

Conformal removability of SLE $_{4}$

Bipolar oriented random planar maps with large faces and exotic SLE $_{κ} (ρ)$ processes

Regularity of the SLE $_{4}$ uniformizing map and the SLE $_{8}$ trace