The `conifold gap' conjecture asserts that the polar part of the Gromov-Witten potential of a Calabi-Yau threefold near its conifold locus has a universal expression described by the logarithm of the Barnes G-function. In this talk I will describe a proof of the Conifold Gap Conjecture for the local projective plane, whereby the higher genus conifold Gromov-Witten generating series of local P2 are related to the thermodynamics of a certain statistical mechanical ensemble of repulsive particles on the positive half-line. As a corollary, this establishes the all-genus mirror principle for local P2 through the direct integration of the BCOV holomorphic anomaly equations.