Interest originally sparked by the discussion Discussion about Hairer's existence theory for stochastic differential equations (BTW, the discussion happpened days before Hairer was awarded the Fields prize!), and given that I'm still finding Hairer's own introduction to the subject "Introduction to regularity structures" incomprehensible (for one, I have zero knowledge on stochastic PDE), I'd like to ask in my situation what would be a recommendable learning path, to the end of understanding its relevance to QFT/renormalization?

Here's some of my relevant background:

1. Quite familiar with statistical mechanics/QFT/renormalization in the physicist style (but barely knows any operator product expansion technique), near zero exposure to constructive QFT in mathematics literatures.

2. Have some brief exposure to measure theory and functional analysis, i.e., I studied extensively the terse little book by Komolgorov and Fomin, very little distribution theory was included in there.

3. Zero knowledge on probability/stochastic theories.

Again, life might be too short to fully master Hairer's theory as a physicist, for now I can only wish to study it to the extent of understanding its relevance to QFT. Any advice or material recommendation is very welcomed.

And Merry Chirstmas to everyone!