We present our statistical analysis of the connection between active galactic nuclei ( AGN ) variability and physical properties of the central supermassive black hole ( SMBH ) .
We constructed optical light curves using data from the QUEST-La Silla AGN variability survey .
To model the variability , we used the structure function , among the excess variance and the amplitude from Damp Random Walk ( DRW ) modeling .
For the measurement of SMBH physical properties , we used public spectra from the Sloan Digital Sky Survey ( SDSS ) .
Our analysis is based on an original sample of 2345 sources detected in both SDSS and QUEST-La Silla .
For 1473 of these sources we could perform a proper measurement of the spectral and variability properties , and 1348 of these sources were classified as variable ( 91.5 \% ) .
We found that the amplitude of the variability ( A ) depends solely on the rest frame emission wavelength and the Eddington ratio , where A anti-correlates with both \lambda _ { rest } and L / L _ { \text { Edd } } .
This suggests that AGN variability does not evolve over cosmic time , and its amplitude is inversely related to the accretion rate .
We found that the logarithmic gradient of the variability ( \gamma ) does not correlate significantly with any SMBH physical parameter , since there is no statistically significant linear regression model with an absolute value of the slope higher than 0.1 .
Finally , we found that the general distribution of \gamma measured for our sample differs from the distribution of \gamma obtained for light curves simulated from a DRW process .
For 20.6 % of the variable sources in our sample , a DRW model is not appropriate to describe the variability , since \gamma differs considerably from the expected value of 0.5 .