A sprinkled decoupling inequality for Gaussian processes and applications
A sprinkled decoupling inequality for Gaussian processes and applications
We establish the sprinkled decoupling inequality P[X∈A1∩A2]−P[X+ε∈A1]P[X+ε∈A2]≤c‖KI1,I2‖∞ ε2, where X is an arbitrary Gaussian vector, A1 and A2 are increasing events that depend on coordinates I1 and I2 respectively, ε>0 is a sprinkling parameter, ‖KI1,I2‖∞ is the maximum absolute covariance between coordinates of X in I1 and I2, and c>0 …