  Understanding and modeling the dynamics of pedestrian crowds can help with
designing and increasing the safety of civil facilities. A key feature of
crowds is its intrinsic stochasticity, appearing even under very diluted
conditions, due to the variability in individual behaviours. Individual
stochasticity becomes even more important under densely crowded conditions,
since it can be nonlinearly magnified and may lead to potentially dangerous
collective behaviours. To understand quantitatively crowd stochasticity, we
study the real-life dynamics of a large ensemble of pedestrians walking
undisturbed, and we perform a statistical analysis of the fully-resolved
pedestrian trajectories obtained by a year-long high-resolution measurement
campaign. Our measurements have been carried out in a corridor of the Eindhoven
University of Technology via a combination of Microsoft Kinect 3D-range sensor
and automatic head-tracking algorithms. The temporal homogeneity of our large
database of trajectories allows us to robustly define and separate average
walking behaviours from fluctuations parallel and orthogonal with respect to
the average walking path. Fluctuations include rare events when individuals
suddenly change their minds and invert their walking direction. Such tendency
to invert direction has been poorly studied so far even if it may have
important implications on the functioning and safety of facilities. We propose
a novel model for the dynamics of undisturbed pedestrians, based on stochastic
differential equations, that provides a good agreement with our experimental
observations, including the occurrence of rare events.
