A sorting network (also known as a reduced decomposition of the reverse permutation), is shortest path from $12 \cdots n$ to $n 21$ in Cayley graph symmetric group $S_n$ generated by adjacent transpositions. We prove that uniform random $n$-element $\sigma^n$, all particle trajectories are close sine curves with high probability. also find weak limit time-$t$ permutation matrix measures $\sigma...

We present several results on the compactness of space morphisms between analytic spaces in sense Berkovich. show that under certain conditions source, every sequence maps having an affinoid target has a subsequence converges pointwise to continuous map. also study class arise this way. Locally, they turn be after base change. Our naturally lead definition normal families. give some application...

We prove non-archimedean analogue of Sendov’s conjecure. also provide complete list polynomials over an algebraically closed field $$K$$ that satisfy the optimal bound in conjecture.