Related papers: How does the supercritical GMC converge?
We consider the problem of critical gravitational collapse of a scalar field in 2+1 dimensions with spherical (circular) symmetry. After surveying all the analytic, continuously self-similar solutions and considering their global structure,…
We consider Gaussian multiplicative chaos measures defined in a general setting of metric measure spaces. Uniqueness results are obtained, verifying that different sequences of approximating Gaussian fields lead to the same chaos measure.…
In this article we systematically study the general properties and the single-point moments of the inverse of the Gaussian multiplicative chaos.
The complex Gaussian Multiplicative Chaos (or complex GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is a log correlated Gaussian field on $\mathbb R^d$ and $\gamma=\alpha+i\beta$ is a complex…
We consider the supersymmetric approach to gaussian disordered systems like the random bond Ising model and Dirac model with random mass and random potential. These models appeared in particular in the study of the integer quantum Hall…
The braking torque that dictates the timing properties of magnetars is closely tied to the large-scale dipolar magnetic field on their surface. The formation of this field has been a topic of ongoing debate. One proposed mechanism, based on…
We review recent progress relating to the extreme value statistics of the characteristic polynomials of random matrices associated with the classical compact groups, and of the Riemann zeta-function and other $L$-functions, in the context…
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…
Interacting physical systems in the neighborhood of criticality (and massive continuum field theories) can often be characterized by just two physical scales: a (macroscopic) correlation length and a (microscopic) interaction range, related…
The auto-correlation between two members of a galaxy population is symmetric under the interchange of the two galaxies being correlated. The cross-correlation between two different types of galaxies, separated by a vector $\bf{r}$, is not…
One of the main problems in the studies of large scale galaxy structures concerns the relation of the correlation properties of a certain population of objects with those of a selected subsample of it, when the selection is performed by…
We present the findings of an investigation of critical behavior in the collapse of spherically symmetric distributions of massive scalar field. Two distinct types of phase transition are observed at the verge of black hole formation and a…
Cosmological theories suggest that the angular momentum of galaxies should be closely linked to the structure of the cosmic web. The Local Supercluster is the closest and most studied structure where the orientation of galaxy spins can be…
We discuss a Gaussian multiplicative chaos (GMC) structure underlying a family of random measures $\mathbf{M}_r$, indexed by $r\in\mathbb{R}$, on a space $\Gamma$ of directed pathways crossing a diamond fractal with Hausdorff dimension two.…
(Abridged). We model gravitational instability in a wide range of isolated disk galaxies, using GADGET, a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and…
We consider a sub-critical Gaussian multiplicative chaos (GMC) measure defined on the unit interval [0,1] and prove an exact formula for the fractional moments of the total mass of this measure. Our formula includes the case where…
The interplay between disorder, quantum fluctuations and dissipation is studied in the random transverse Ising chain coupled to a dissipative Ohmic bath with a real space renormalization group. A typically very large length scale, L*, is…
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chru\'sciel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change…
We show that, for general convolution approximations to a large class of log-correlated fields, including the 2d Gaussian free field, the critical chaos measures with derivative normalisation converge to a limiting measure {\mu}'. This…
The "direct collapse" scenario has emerged as a promising evolutionary track for the formation of supermassive black holes early in the Universe. In an idealized version of such a scenario, a uniformly rotating supermassive star spinning at…