Personne

Juhan Aru

Percolation for 2D Classical Heisenberg Model and Exit Sets of Vector Valued GFF

Our motivation in this paper is twofold. First, we study the geometry of a class of exploration sets, called exit sets, which are naturally associated with a 2D vector-valued Gaussian Free Field:

\phi : \mathbb{Z}^2 \rightarrow \mathbb{R}^N

N \ge 1

. W ...

SPRINGER2025

Noise-like analytic properties of imaginary chaos

Juhan Aru

In this note we continue the study of imaginary multiplicative chaos µβ:= exp(iβΓ), where Γ is a two-dimensional continuum Gaussian free field. We concentrate here on the fine-scale analytic properties of |µβ (Q(x, r))| as r → 0, where Q(x, r) is a square ...

2025

The density of imaginary multiplicative chaos is positive

Juhan Aru, Antoine Pierre François Jego

Consider a log-correlated Gaussian field Γ and its associated imaginary multiplicative chaos: eiβΓ: where β is a real parameter. In [3], we showed that for any nonzero test function f, the law of∫ f: eiβΓ: possesses a smooth density with respect to Lebesgu ...

2024

Thick points of the planar GFF are totally disconnected for all & gamma;=6 0*

Juhan Aru

We prove that the set of-y-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all-y =6 0. Our proof relies on the coupling between a GFF and the nested CLE4. In particular, we show that th ...

INST MATHEMATICAL STATISTICS-IMS2023

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

Juhan Aru

We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition o ...

ECOLE POLYTECHNIQUE2022

Density of imaginary multiplicative chaos via Malliavin calculus

Juhan Aru, Janne Matias Junnila

We consider the imaginary Gaussian multiplicative chaos, i.e. the complex Wick exponential mu(beta ):=: e(i beta Gamma(x)) : for a log-correlated Gaussian field Gamma in d >= 1 dimensions. We prove a basic density result, showing that for any nonzero conti ...

SPRINGER HEIDELBERG2022

Brownian half-plane excursion and critical Liouville quantum gravity

Juhan Aru, Xin Sun

In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be obtained by gluing together a pair of Brownian motions. In this paper, we study the coun ...

WILEY2022

Extremal Distance And Conformal Radius Of A Cle4 Loop

Juhan Aru, Titus Lupu

Consider CLE4 in the unit disk, and let l be the loop of the CLE4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by l. We complement their result by determining ...

INST MATHEMATICAL STATISTICS-IMS2022

Reconstructing the base field from imaginary multiplicative chaos

Juhan Aru, Janne Matias Junnila

We show that the imaginary multiplicative chaos exp(i beta Gamma) determines the gradient of the underlying field Gamma for all log-correlated Gaussian fields with covariance of the form -log|x-y|+g(x,y) with mild regularity conditions on g, for all d >= 2 ...

WILEY2021

Gaussian Multiplicative Chaos Through the Lens of the 2D Gaussian Free Field

Juhan Aru

The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical regime. By consid ...

POLYMAT2020

Percolation for 2D Classical Heisenberg Model and Exit Sets of Vector Valued GFF

Juhan Aru

Our motivation in this paper is twofold. First, we study the geometry of a class of exploration sets, called exit sets, which are naturally associated with a 2D vector-valued Gaussian Free Field:

\phi : \mathbb{Z}^2 \rightarrow \mathbb{R}^N

N \ge 1

. W ...

SPRINGER2025