TITLE: Recent impressive combinatorial developments in probability theory
QUESTION [7 upvotes]: In the preface to the second edition of Daniel Stroock's book "Probability Theory: An Analytic View", there is this striking claim (on p. xv)

... I suspect that, for at least a decade, the most important developments in the field will have a strong combinatorial component ...

I have several questions

What have been the most striking and impressive developments along that line in the past decade?
Is there an overwhelming agreement in the research community about that statement?
What are the most promising avenues of exploration?
Was the progress occurring throughout probability theory and some specific fields such as stochastic processes or statistics or was it confined to areas that were fundamentally combinatorial in nature such as random graph theory?

REPLY [7 votes]: A whole body of results in probability with strong combinatorial flavour are around 2-dimensional stochastic models. Some of this progress started 15 years ago but much was achieved in the last decade. Much of this research has combinatorial flavour. This includes conformal invariance for planar percolation on the triangular grid; The stochastic Lowevner equations, SLE, and their relations with Brownian motion, crirical percolation, loop-erased random walks, the Ising model, and other models. These relations allowed the computation of many critical exponents of 2D models. You can add to that the recent results on self avoiding random walks (again in 2D), and the computation of critical probabilities for 2D Potts model.

REPLY [4 votes]: Another important development in probability theory with strong combinatorial flavour and  relations to mathematical physics is around random partitions. This is closely related to random surfaces and random matrices. The origin are again older but much was achieved in the last decade or so.