Research
We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite planar…
Noise sensitivity concerns the phenomenon that certain types of events (Boolean functions) are sensitive to small noise. This topic is related to the notion of influence, which is a way to specify the importance of…
In 1870 Schroeder introduced four problems concerning the enumeration of bracketings of words or sets of a given size. We will consider what uniform draws from these bracketings look like as the size of the…
We consider a mean field linear-quadratic-Gaussian game with a major player and a large number of minor players parametrized by a continuum set. The mean field generated by the minor players is approximated by a…
The star-triangle transformation was `discovered’ in 1899. It has since become one of the basic tools for studying disordered systems in two dimensions, and it is known amongst physicists as the `Yang-Baxter equation’. We shall…
By Rob Knies, Managing Editor, Microsoft Research At 5:46 p.m. on Sept. 20, Georges Gonthier, principal researcher at Microsoft Research Cambridge, sent a brief email to his colleagues at the Microsoft Research-Inria Joint Centre in…
