Zobrazeno 1 - 10
of 96
pro vyhledávání: '"Aru, Juhan"'
A martingale-type of characterisation of the Gaussian free field and fractional Gaussian free fields
Autor:
Aru, Juhan, Woessner, Guillaume
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 stochastic heat equation and to fractional stochastic heat equations. The main
Externí odkaz:
http://arxiv.org/abs/2407.16261
Autor:
Aru, Juhan, Bordereau, Philémon
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 $\sigma$-finite measure on curves; yet it is in general not clear how to construct suc
Externí odkaz:
http://arxiv.org/abs/2405.20148
Autor:
Aru, Juhan, Korzhenkova, Aleksandra
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 related via the discrete Gaussian free field (GFF). More precisely, using probabilistic limit theorems an
Externí odkaz:
http://arxiv.org/abs/2405.04501
Consider a log-correlated Gaussian field $\Gamma$ and its associated imaginary multiplicative chaos $:e^{i \beta \Gamma}:$ where $\beta$ is a real parameter. In [AJJ22], we showed that for any nonzero test function $f$, the law of $\int f :e^{i \beta
Externí odkaz:
http://arxiv.org/abs/2403.05289
In this note we continue the study of imaginary multiplicative chaos $\mu_\beta := \exp(i \beta \Gamma)$, where $\Gamma$ is a two-dimensional continuum Gaussian free field. We concentrate here on the fine-scale analytic properties of $|\mu_\beta(Q(x,
Externí odkaz:
http://arxiv.org/abs/2401.14942
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 the Brownian motion, and on the other hand can be seen as an FK represe
Externí odkaz:
http://arxiv.org/abs/2304.03150
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 : $\phi : Z^2 \to R^N, N\geq 1$. We prove that, somewhat surprisingly,
Externí odkaz:
http://arxiv.org/abs/2212.06767
We prove that the set of $\gamma$-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all $\gamma \neq 0$. Our proof relies on the coupling between a GFF and the nested CLE$_4$. In pa
Externí odkaz:
http://arxiv.org/abs/2209.04247
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 the mating of two continuum random trees. In this paper, we consider
Externí odkaz:
http://arxiv.org/abs/2109.00275
Autor:
Aru, Juhan, Powell, Ellen
We prove that under certain mild moment and continuity assumptions, the $d$-dimensional Gaussian free field is the only stochastic process in $d\geq 2$ that is translation invariant, exhibits a certain scaling, and satisfies the usual domain Markov p
Externí odkaz:
http://arxiv.org/abs/2103.07273