A New Condition for the Invariance Principle for Stationary Random   Fields
  We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance principles for orthomartingales and functionals of linear random fields. 
Yizao Wang and Michael Woodroofe
math.PR math.ST stat.TH