46 citations · 204 across the 20 of their papers we have counts for
24 papers
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…
SLE and its partition function in multiply connected domains via the Gaussian Free Field and restriction measures
Juhan Aru, Philémon 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 -finite measu…
The Spherical model and the large- limit of the Spin model via the Gaussian free field
Juhan Aru, Aleksandra Korzhenkova
We revisit the relation between the spherical model of Berlin-Kac and the spin model in the limit , and explain how they are connected via the discrete Gaussia…
The density of imaginary multiplicative chaos is positive
Juhan Aru, Antoine Jego, Janne Junnila
Consider a log-correlated Gaussian field and its associated imaginary multiplicative chaos where is a real parameter. In [AJJ22], we showed that for any nonzer…
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 , where is a two-dimensional continuum Gaussian free field. We concentrate here on the fi…
Excursion decomposition of the 2D continuum GFF
Juhan Aru, Titus Lupu, Avelio Sepúlveda
In this note we show that the 2D continuum Gaussian free field (GFF) admits an excursion decomposition that is on the one hand similar to the classical excursion decomposition of t…
Percolation for 2D classical Heisenberg model and exit sets of vector valued GFF
Juhan Aru, Christophe Garban, Avelio Sepúlveda
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 GFF :…
Thick points of the planar GFF are totally disconnected for all
Juhan Aru, Léonie Papon, Ellen Powell
We prove that the set of -thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all . Our proof relies…
Mating of trees for critical Liouville quantum gravity
Juhan Aru, Nina Holden, Ellen Powell +1
In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be described by…
A characterisation of the continuum Gaussian free field in dimensions
Juhan Aru, Ellen Powell
We prove that under certain mild moment and continuity assumptions, the -dimensional Gaussian free field is the only stochastic process in that is translation invarian…
Density of imaginary multiplicative chaos via Malliavin calculus
Juhan Aru, Antoine Jego, Janne Junnila
We consider the imaginary Gaussian multiplicative chaos, i.e. the complex Wick exponential for a log-correlated Gaussian field in dimensions. We…
Reconstructing the base field from imaginary multiplicative chaos
Juhan Aru, Janne Junnila
We show that the imaginary multiplicative chaos determines the gradient of the underlying field for all log-correlated Gaussian fields with covariance of the form $…
Extremal distance and conformal radius of a CLE_4 loop
Juhan Aru, Titus Lupu, Avelio Sepúlveda
Consider CLE in the unit disk and let be the loop of the CLE surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen fr…
The first passage sets of the 2D Gaussian free field: convergence and isomorphisms
Juhan Aru, Titus Lupu, Avelio Sepúlveda
In a previous article, we introduced the first passage set (FPS) of constant level of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. In…
Exceptional graphs for the random walk
Juhan Aru, Carla Groenland, Tom Johnston +3
If is the simple random walk on the square lattice , then induces a random walk on any spanning subgraph $G\subset \mathbb…
Critical Liouville measure as a limit of subcritical measures
Juhan Aru, Ellen Powell, Avelio Sepúlveda
We study how the Gaussian multiplicative chaos (GMC) measures corresponding to the 2D Gaussian free field change when approaches the critical parameter . In particular…
Two-valued local sets of the 2D continuum Gaussian free field: connectivity, labels, and induced metrics
Juhan Aru, Avelio Sepúlveda
We study two-valued local sets, , of the two-dimensional continuum Gaussian free field (GFF) with zero boundary condition in simply connected domains. Intuitivel…
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) m…
First passage sets of the 2D continuum Gaussian free field
Juhan Aru, Titus Lupu, Avelio Sepúlveda
We introduce the first passage set (FPS) of constant level of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set…
Balancing sums of random vectors
Juhan Aru, Bhargav Narayanan, Alex Scott +1
We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition thes…
On bounded-type thin local sets of the two-dimensional Gaussian free field
Juhan Aru, Avelio Sepúlveda, Wendelin Werner
We study certain classes of local sets of the two-dimensional Gaussian free field (GFF) in a simply-connected domain, and their relation to the conformal loop ensemble CLE(4) and i…
Two perspectives of the 2D unit area quantum sphere and their equivalence
Juhan Aru, Yichao Huang, Xin Sun
2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in stud…
Multiagent Cooperation and Competition with Deep Reinforcement Learning
Ardi Tampuu, Tambet Matiisen, Dorian Kodelja +5
Multiagent systems appear in most social, economical, and political situations. In the present work we extend the Deep Q-Learning Network architecture proposed by Google DeepMind t…
KPZ relation does not hold for the level lines and the SLE flow lines of the Gaussian free field
Juhan Aru
In this paper we mingle the Gaussian free field, the Schramm-Loewner evolution and the KPZ relation in a natural way, shedding new light on all of them. Our principal result shows…