New paper on arXiv: A conformal Skorokhod embedding

I’m happy to say that I recently uploaded a paper to the arXiv under the title “A conformal Skorokhod embedding” (https://arxiv.org/abs/1905.00852). In this post, I’d like to explain what the Skorokhod embedding problem is, how I came across it, some previously known solutions, and my own tiny contribution. But really, all of this is just … More New paper on arXiv: A conformal Skorokhod embedding

Converging Bernoulli Series

Here is a silly little question that my friend Ori and I ran into. Let be a decreasing sequence of positive real numbers which tends to 0. Perhaps in a more decent universe, the sum would always equal some finite number, but already in kindergarten we learn that that’s not true: For example, the partial … More Converging Bernoulli Series

Arithmetic progressions in space?

Here is a neat question that I stumbled upon during my academic random walk. A sequence of vectors is called an arithmetic progression of length k if there exists a vector such that . In other words, an arithmetic progression in is exactly the generalization you would expect of your good ol’ high-school arithmetic progression … More Arithmetic progressions in space?

There and back again, part 3

This is part three in a three-part series about recurrence and transience on the integer lattices. Here is part one. Here is part two. Weary and tired, we are approaching the end of our coin-flipping, lattice-exploring adventures, but with one aching question still burning deep within our hearts: Is the random walk on the three-dimensional … More There and back again, part 3

There and back again, part 2

This is part two in a three-part series about recurrence and transience on the integer lattices. Here is part one. Here is part three. In the previous post, we saw that the integer lattice is recurrent. This means that a simple random walk, when starting at the origin , will return to the origin with … More There and back again, part 2

There and back again, part 1

This is part one in a three-part series about recurrence and transience on the integer lattices. Here is part two. Here is part three. It is a truth universally acknowledged, that a single man in possession of a coin, who repeatedly flips it, taking one step forwards if it comes up heads, and one step … More There and back again, part 1

New paper on arXiv: Decomposition of mean-field Gibbs distributions into product measures

I’m happy to say that my advisor Ronen Eldan and I recently uploaded a paper to the arXiv under the title “Decomposition of mean-fields Gibbs distributions into product measures” (https://arxiv.org/abs/1708.05859). This is a sister paper of the previous one about exponential random graphs: this one presents a “general framework” and only briefly touches on how … More New paper on arXiv: Decomposition of mean-field Gibbs distributions into product measures