Related papers: How does the supercritical GMC converge?
In this paper, we consider the Gibbs measure associated to a logarithmically correlated random potential (including two dimensional free fields) at low temperature. We prove that the energy landscape freezes and enters in the so-called…
Gibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many…
Gaussian multiplicative chaos (GMC) is a canonical random fractal measure obtained by exponentiating log-correlated Gaussian processes, first constructed in the seminal work of Kahane (1985). Since then it has served as an important…
We study the zeroes of a family of random holomorphic functions on the unit disc, distinguished by their invariance with respect to the hyperbolic geometry. Our main finding is a transition in the limiting behaviour of the number of zeroes…
We study the singularity created in the supercritical collapse of a spherical massless scalar field. We first model the geometry and the scalar field to be homogeneous, and find a generic solution (in terms of a formal series expansion)…
Recently, we have shown that if the ISM is governed by super-sonic turbulent flows, the excursion-set formalism can be used to calculate the statistics of self-gravitating objects over a wide range of scales. On the largest self-gravitating…
In the present paper, we show that (under some minor technical assumption) Complex Gaussian Multiplicative Chaos defined as the complex exponential of a $\log$-correlated Gaussian field can be obtained by taking the limit of the exponential…
This article reviews classical and quantum aspects of critical phenomena in gravitational collapse. We pay special attention to the origin of the scaling law for black hole mass, and to phase transitions in which black hole formation turns…
The supercritical state is currently viewed as uniform on the pressure-temperature phase diagram. Supercritical fluids have the dynamic motions of a gas but are able to dissolve materials like a liquid. They have started to be deployed in…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
We study how the Gaussian multiplicative chaos (GMC) measures $\mu^\gamma$ corresponding to the 2D Gaussian free field change when $\gamma$ approaches the critical parameter $2$. In particular, we show that as $\gamma\to 2^{-}$,…
We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic…
We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with…
We study the properties of ultra-compact spherically symmetric dark matter sector star objects, being the solution of Einstein equations with two $U(1)$-gauge fields. One of them is the ordinary Maxwell field, while the auxiliary gauge…
Recognizing the regime of positive definiteness for a strictly logarithmic covariance kernel, we prove that the small deviations of a related Gaussian multiplicative chaos (GMC) $M_\gamma$ are for each natural dimension $d$ always of…
A satisfactory understanding of the origin of the dependence of galaxy properties on their environment has remained, so far, out of reach. In the light of numerous observational results and substantial theoretical progress obtained for…
We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that…
Gaussian Multiplicative Chaos (GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is Gaussian field on $\mathbb R^d$ (or an open subset of it) whose correlation function is of the form $ K(x,y)= \log…
The equilibrium properties of classical self-gravitating systems in the grand canonical ensemble are studied by using the correspondence with an euclidean field theory with infrared and ultraviolet cutoffs. It is shown that the system…
We introduce a simple model to explore the star formation histories of disk galaxies. We assume that the disk origins and grows by continuous gas infall. The gas infall rate is parametrized by the Gaussian formula with one free parameter:…