  How long does a diffusing molecule spend in a close vicinity of a confining
boundary or a catalytic surface? This quantity is determined by the boundary
local time, which plays thus a crucial role in the description of various
surface-mediated phenomena such as heterogeneous catalysis, permeation through
semi-permeable membranes, or surface relaxation in nuclear magnetic resonance.
In this paper, we obtain the probability distribution of the boundary local
time in terms of the spectral properties of the Dirichlet-to-Neumann operator.
We investigate the short-time and long-time asymptotic behaviors of this random
variable for both bounded and unbounded domains. This analysis provides
complementary insights onto the dynamics of diffusing molecules near partially
reactive boundaries.
