In recent papers, McLeish and others have obtained invariance principles for weak convergence of martingales to Brownian motion. We generalize these results to prove that solutions of discrete-time ...

Many discrete martingales with increments in L 2 can be normalized so that the resulting trajectory is distributed approximately like Brownian motion. This paper will find all such martingales, ...

Symmetry and invariance lie at the heart of modern physical theories, serving as guiding principles in our understanding of the natural world. These ideas are central to elucidating conservation laws ...

When Lisa Piccirillo solved a decades-old mystery about the “Conway knot,” she had to overcome the knot’s uncanny ability to hoodwink some of the most powerful tools mathematicians have devised. Known ...