We study the heat kernel and the Green’s function on the infinite supercritical percolation cluster in dimension d ≥ 2 and prove a quantitative homogenization theorem for these functions with an ...

IN the preface to his "Elliptic Functions", written in 1892, Prof. A. G. Greenhill complained that, although the subject was then nearly seventy years old, it had not made its way into the ordinary ...

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...