A spectral gap is a positive separation between distinguished spectral values and the remaining operator spectrum
of a linear operator. For a self-adjoint
Markov linear operator generator 
with stationary probability
measure 
, the gap above the constant functions is characterized by
 |
The infimum is over functions in the generator domain with nonzero variance. The reciprocal is the optimal variance-form
Poincaré inequality constant
for this energy. For a positive transfer operator 
with 
whose vacuum vector 
has eigenvalue
1, the mass-gap convention is 
. Its clock
or lattice time unit is part of the normalization.
