Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Junnila, Janne"'
Piecewise geodesic Jordan curves II: Loewner energy, projective structures, and accessory parameters
Consider a Jordan curve on the Riemann sphere passing through $n \ge 3$ given points. We show that in each relative isotopy class of such curves, there exists a unique curve that minimizes the Loewner energy. These curves have the property that each
Externí odkaz:
http://arxiv.org/abs/2410.22275
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
We prove that multiplicative chaos measures can be constructed from extreme level sets or thick points of the underlying logarithmically correlated field. We develop a method which covers the whole subcritical phase and only requires asymptotics of s
Externí odkaz:
http://arxiv.org/abs/2209.06548
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 $d \geq 1$ dimensions. We prove a basic density result, showing that for
Externí odkaz:
http://arxiv.org/abs/2008.11768
Autor:
Aru, Juhan, Junnila, Janne
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 o
Externí odkaz:
http://arxiv.org/abs/2006.05917
Denote by $\mu_\beta="\exp(\beta X)"$ the Gaussian multiplicative chaos which is defined using a log-correlated Gaussian field $X$ on a domain $U\subset\mathbb{R}^d$. The case $\beta\in\mathbb{R}$ has been studied quite intensively, and then $\mu_\be
Externí odkaz:
http://arxiv.org/abs/1905.12027
In this article we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorem
Externí odkaz:
http://arxiv.org/abs/1808.06838
In this article we study imaginary Gaussian multiplicative chaos -- namely a family of random generalized functions which can formally be written as $e^{i X(x)}$, where $X$ is a log-correlated real-valued Gaussian field on $\mathbb{R}^d$, i.e. it has
Externí odkaz:
http://arxiv.org/abs/1806.02118
Publikováno v:
Communications on Pure & Applied Mathematics; Nov2024, Vol. 77 Issue 11, p4212-4286, 75p
