Rigorous quantum field theory functional integrals over the p-adics:   research announcement
  In this short note we announce the construction of scale invariant non-Gaussian generalized stochastic processes over three dimensional p-adic space. The construction includes that of the associated squared field and our result shows this squared field has a dynamically generated anomalous dimension which rigorously confirms a prediction made more than forty years ago, in an essentially identical situation, by Kenneth G. Wilson. We also prove a mild form of universality for the model under consideration. 
Abdelmalek Abdesselam, Ajay Chandra, Gianluca Guadagni
math.PR hep-th math-ph math.MP math.NT