A note on the coefficients of Rawnsley's epsilon function of Cartan-Hartogs domains

We extend a result of Z. Feng and Z. Tu by showing that if one of the coefficients $a_j$, $2\leq j\leq n$, of Rawnlsey's epsilon function associated to a $n$-dimensional Cartan-Hartogs domain is constant, then the domain is biholomorphically equivalent to the complex hyperbolic space.Comment: 6 p

Collisions versus stellar winds in the runaway merger scenario: place your bets

The runaway merger scenario is one of the most promising mechanisms to explain the formation of intermediate-mass black holes (IMBHs) in young dense star clusters (SCs). On the other hand, the massive stars that participate in the runaway merger lose mass by stellar winds. This effect is tremendously important, especially at high metallicity. We discuss N-body simulations of massive (~6x10^4 Msun) SCs, in which we added new recipes for stellar winds and supernova explosion at different metallicity. At solar metallicity, the mass of the final merger product spans from few solar masses up to ~30 Msun. At low metallicity (0.01-0.1 Zsun) the maximum remnant mass is ~250 Msun, in the range of IMBHs. A large fraction (~0.6) of the massive remnants are not ejected from the parent SC and acquire stellar or black hole companions. Finally, I discuss the importance of this result for gravitational wave detection.Comment: 4 pages, 3 figures, 1 table, to appear in Memorie della SAIt (proceedings of the Modest 16 conference, 18-22 April 2016, Bologna, Italy

Long time asymptotics of a Brownian particle coupled with a random environment with non-diffusive feedback force

We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle has bounded (in time) variance when the particle interacts with a subdiffusive field; when the interaction is with a superdiffusive field the variance of the limiting process grows in time as t^{2{\gamma}-1}, 1/2 < {\gamma} < 1. Two different kinds of superdiffusing (random) environments are considered: one is described through the use of the fractional Laplacian; the other via the Riemann-Liouville fractional integral. The subdiffusive field is modeled through the Riemann-Liouville fractional derivative.Comment: 45 page