Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials

We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in $\mathbb{R}^d$ and interacting via logarithmic functions (two-dimensional Coulomb potentials). These potentials are very strong and act over a long range in nature. The associated equilibrium states are no longer Gibbs measures. We present general results for the construction of such diffusions and, as applications thereof, construct two typical interacting Brownian motions with logarithmic interaction potentials, namely the Dyson model in infinite dimensions and Ginibre interacting Brownian motions. The former is a particle system in $\mathbb{R}$, while the latter is in $\mathbb{R}^2$. Both models are translation and rotation invariant in space, and as such, are prototypes of dimensions $d=1,2$, respectively. The equilibrium states of the former diffusion model are determinantal or Pfaffian random point fields with sine kernels. They appear in the thermodynamical limits of the spectrum of the ensembles of Gaussian random matrices such as GOE, GUE and GSE. The equilibrium states of the latter diffusion model are the thermodynamical limits of the spectrum of the ensemble of complex non-Hermitian Gaussian random matrices known as the Ginibre ensemble.Comment: Published in at http://dx.doi.org/10.1214/11-AOP736 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Community reactions to aircraft noise in the vicinity of airport: A comparative study of the social surveys using interview method

A comparative study was performed on the reports of community reactions to aircraft noise. The direct and immediate reactions to aircraft noise such as perceived noisiness, interference with conversations, etc. and various emotional influences were most remarkable; indirect and long term influences such as disturbance of mental work and physical symptoms were less remarkable

Event-by-event mean pTp_{\rm T} fluctuations and transverse size of color flux tube generated in pp-pp collisions at s\sqrt{s}=0.90TeV

We propose a novel phenomenological model of mean transverse momentum fluctuations based on the Geometrical Scaling hypothesis. Bose-Einstein correlations between two gluons generated from an identical color flux tube are taken into account as a source of the fluctuation. We calculate an event-by-event fluctuation measure $\sqrt{C_m}/\langle p_{\rm T}\rangle$ and show that ALICE data observed at $\sqrt s=$0.90 TeV for $p$+$p$ collisions are reproduced. By fitting our model to the experimental data, we evaluate the transverse size of the color flux tube as a function of the multiplicity.Comment: 14 pages, 7 figure

Infinite-dimensional stochastic differential equations arising from Airy random point fields

We identify infinite-dimensional stochastic differential equations (ISDEs) describing the stochastic dynamics related to Airy$_{\beta }$ random point fields with $\beta =1,2,4$. We prove the existence of unique strong solutions of these ISDEs. When $\beta = 2$, this solution is equal to the stochastic dynamics defined by the space-time correlation functions obtained by Spohn and Johansson among others. We develop a new method to construct a unique, strong solution of ISDEs. We expect that our approach is valid for other soft-edge scaling limits of stochastic dynamics arising from the random matrix theory.Comment: 55 page