deletions | additions       diff --git a/CAR Generation.tex b/CAR Generation.tex  index df98913..381244d 100644  --- a/CAR Generation.tex  +++ b/CAR Generation.tex 
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The optical light curve of quasars are generated by fluctuations in the brightness of the accretion disk with structure in the time series on the order of days [REFS]. Since these fluctuations are coherent, the implication is that the size of the accretion disk is roughly $R_{\rm src} \sim 10^{16}$ cm (which will be important for the microlensing calculation in \S \ref{sec:microlensing}). These fluctuations have been shown to be well described by a Continuous Auto Regressive (CAR) process. First described by [REFS], the CAR process is a damped random walk and is equivalent to a Gaussian Process in which the covariance between two points on the light curve decreases as a function of their temporal separation. Using data from the MACHO survey [REF], [REF] fit a CAR process to {\bf (GGD: how many???)} r-band MACHO quasar light curves. The CAR process is given by [see Appendix in REFS],  \begin{equation}  M(t) = e^{-t/\tau} M(0) + b\tau(1-e^{-t/\tau}) \langle M \rangle(1-e^{-t/\tau})  + \sigma\int_{0}^{t} e^{-(t-s)/\tau} dB(s), \end{equation}  where $M$ is the magnitude of an image, $\tau$ is a characteristic timescale in days, and $\sigma$ is the characteristic amplitude of the fluctuations in mag/day$^{1/2}$.