7 problems

A Baxter permutation of size $n$ is a permutation avoiding the two patterns specified in the source, and bipolar-oriented planar maps with general face degrees correspond to Baxter…

Let $\mathbb{X}\subset\mathbb{S}^2$ be the embedded random surface, and let $\mathbb{X}'$ be an independent copy of $\mathbb{X}$. A neighborhood of $\mathbb{X}$ means a neighborhoo…

Let $a\from (2,5/2)$, let $\bigl(f_i\bigr)_{i\geq 1}$ be the sampled marked vertices or faces, let $d^\dagger_\mathrm{gr}$ denote the graph distance, and let…

Let $a\from (3/2,5/2)$, let $\bigl(f_i\bigr)_{i\geq 1}$ be the sampled marked vertices or faces, let $d^\dagger_\mathrm{fpp}$ denote the first-passage percolation distance, and let…

A planar linear normal $\lambda$-term is a linear normal $\lambda$-term whose syntactic diagram is planar; call it 3-connected when its syntactic diagram is 3-connected. For…

Let $Q_\infty$ be the uniform infinite planar quadrangulation (UIPQ), rooted at $\rho$, and consider simple random walk on its vertices. A graph is recurrent when simple random wal…

Let $Q_\infty$ be the uniform infinite planar quadrangulation (UIPQ), rooted at $\rho$, and let $(X_k)_{k\geq 0}$ be simple random walk on $Q_\infty$ started at $\rho$. Write…