Related papers: Phase Transitions in Gravitational Allocation
We discuss the statistical mechanics of a system of self-gravitating particles with an exclusion constraint in position space in a space of dimension $d$. The exclusion constraint puts an upper bound on the density of the system and can…
For d>=3, we construct a non-randomized, fair and translation-equivariant allocation of Lebesgue measure to the points of a standard Poisson point process in R^d, defined by allocating to each of the Poisson points its basin of attraction…
We prove that the Poisson-Boolean percolation on $\mathbb{R}^d$ undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a $5d-3$ finite moment (in particular we do not assume that the…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
Here, cosmology is obtained from the variable gravitational constant $ G \propto \phi^{-2}$ with $ \phi(x) $ being a scalar and its fluctuations around the ground state. The gravitational action contains Einstein-Hilbert like term with…
We consider a gas of Newtonian self-gravitating particles in two-dimensional space, finding a phase transition, with a high temperature homogeneous phase and a low temperature clumped one. We argue that the system is described in terms of a…
Various theoretical arguments motivate an expectation of a phase transition in matter at extreme densities above nuclear density, accompanied by hopes that gravitational wave observations may reveal the properties of such a transition.…
The possibility of a gravitational phase transition, especially with respect to neutron stars is investigated. First, a semiclassical treatment is given, predicting a gravitational London penetration depth of 12km for neutron stars. Second,…
We study the fluctuations of the largest eigenvalue $\lambda_{\max}$ of $N \times N$ random matrices in the limit of large $N$. The main focus is on Gaussian $\beta$-ensembles, including in particular the Gaussian orthogonal ($\beta=1$),…
We study the distribution of the mean radial displacement of charges of a 2D one-component plasma in the thermodynamic limit $N\to\infty$ at finite temperature $\beta>0$. We compute explicitly the large deviation functions showing the…
Strongly first-order phase transitions, i.e., those with a large order parameter, are characterized by a considerable supercooling and high velocities of phase transition fronts. A very strong phase transition may have important…
We study the evolution of global shapes of galaxies using cosmological simulations. The shapes refer to the components of dark matter (DM), stars and gas at the stellar half-mass radius. Most galaxies undergo a characteristic compaction…
We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…
de Sitter--G\"odel--de Sitter phase transition(dGd) is a possible geometrical phase transition in the very early universe. It induces fluctuations with possibly observable traces on matter and radiation fields. Here we present a simulation…
We set forth a new type of phase transition that might take place in gravitational theories whenever higher-curvature corrections are considered. It can be regarded as a sophisticated version of the Hawking-Page transition, mediated by the…
The phase behavior of stabilized dispersions of macromolecules is most easily described in terms of the effective interaction between the centers of mass of solute particles. For molecules like polymer chains, dendrimers, etc., the…
We analyze in detail a second order phase transition that occurs in large N Gaussian multi-matrix models in which the matrices are constrained to be commuting. The phase transition occurs as the relative masses of the matrices are varied,…
We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of…
Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially…
Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices is formed by the adjacency matrix of an Erd\H{o}s-R\'{e}nyi graph $\mathcal{G}_{n,p}$ equipped with i.i.d.…