Juhan Aru

activity

20242026

collaborators

5 papers

math.PR2026

A martingale-type characterisation of the Gaussian free field and fractional Gaussian free fields

Juhan Aru, Guillaume Woessner

We establish a martingale-type characterisations for the continuum Gaussian free field (GFF) and for fractional Gaussian free fields (FGFs), using their connection to the stochasti…

math.PR2026

SLE and its partition function in multiply connected domains via the Gaussian Free Field and restriction measures

Juhan Aru, PhilÃ©mon Bordereau

One way to uniquely define Schramm-Loewner Evolution (SLE) in multiply connected domains is to use the restriction property. This gives an implicit definition of a $I ¨ $ -finite meas…

math.PR2025

The Spherical model and the large- $N$ limit of the Spin $O (N)$ model via the Gaussian free field

Juhan Aru, Aleksandra Korzhenkova

We revisit the relation between the spherical model of Berlin-Kac and the spin $O (N)$ model in the limit $N \to \infty$ , and explain how they are connected via the discrete Gaussia…

math.PR2025

Noise-like analytic properties of imaginary chaos

Juhan Aru, Guillaume Baverez, Antoine Jego +1

In this note we continue the study of imaginary multiplicative chaos $I^¼_{I^}^{2} := exp (i I^^{2} I^)$ , where $I^$ is a two-dimensional continuum Gaussian free field. We concentrate here on t…

math.PR2024

The density of imaginary multiplicative chaos is positive

Juhan Aru, Antoine Jego, Janne Junnila

Consider a log-correlated Gaussian field $I^$ and its associated imaginary multiplicative chaos $: e^{i I^^{2} I^} :$ where $I^^{2}$ is a real parameter. In [AJJ22], we showed that for any no…