  We discuss the eigenvalue detachment transition in terms of scaling of
fluctuations in ensembles of paths located near convex boundaries of various
physical nature. We consider numerically the BBP-like (Baik-Ben
Arous-P\'ech\'e) transition from the Gaussian to the Tracy-Widom scaling of
fluctuations in several statistical systems for both canonical and
microcanonical ensembles and identify the corresponding control parameter in
each case. In particular, for fixed path length (microcanonical) ensemble of
paths located in the vicinity of a partially permeable semicircle, the
transition occurs at the critical value of a permeability. The Tracy-Widom
regime and the BBP-like transition for fluctuations are discussed in terms of
the Jakiw-Teitelbom (JT) gravity with a radial cutoff which, in turn, has an
interpretation as a ensemble of fixed length world-line geometrically
constrained trajectories of a charged particle in an effective transversal
magnetic field.
