  We provide CoRoT and Spitzer light curves, as well as broad-band
multi-wavelength photometry and high resolution, multi- and single-epoch
spectroscopy for 17 classical T Tauris in NGC 2264 whose CoRoT light curves
(LCs) exemplify the "stochastic" LC class as defined in Cody et al. (2014). The
most probable physical mechanism to explain the optical variability in this LC
class is time-dependent mass accretion onto the stellar photosphere, producing
transient hot spots. As evidence in favor of this hypothesis, multi-epoch high
resolution spectra for a subset of these stars shows that their veiling levels
also vary in time and that this veiling variability is consistent in both
amplitude and timescale with the optical LC morphology. Furthermore, the
veiling variability is well-correlated with the strength of the HeI 6678A
emission line, a feature predicted by models to arise in accretion shocks on or
near the stellar photosphere. Stars with accretion burst LC morphology
(Stauffer et al. 2014) are also attributed to variable mass accretion. Both the
stochastic and accretion burst LCs can be explained by a simple model of
randomly occurring flux bursts, with the stochastic LC class having a higher
frequency of lower amplitude events. Based on their UV excesses, veiling, and
mean Ha equivalent widths, members of the stochastic LC class have only
moderate time-averaged mass accretion rates. The most common feature of their
Ha profiles is for them to exhibit blue-shifted absorption features, most
likely originating in a disk wind. The lack of periodic signatures in the LCs
suggests that little of the variability is due to long-lived hot spots rotating
into or out of our line of sight; instead, the primary driver of the observed
photometric variability is likely to be instabilities in the inner disk that
lead to variable mass accretion.
