From the 1 of 10 linked papers with an AI index.
10 papers
Universality for Random -adic Polynomials and Random Matrices Via the Resultant Distribution Method
Jiahe Shen
We prove universality results for zeros of random -adic polynomials with independent, sufficiently non-concentrated coefficients. We show that when the degree goes to infinity,…
Hitting time mixing for random -cycles
Chen Shang, Jiahe Shen, Jiyue Zeng +1
In this paper, we study the random walk on the symmetric group generated by the conjugacy class of -cycles, where . We prove that the wa…
-adic Sum-Product, Projections, and Furstenberg Sets
Jiahe Shen
The paper proves sharp lower bounds for the Hausdorff dimension of Furstenberg sets in the p‑adic plane, and derives related p‑adic projection theorems and discretized sum‑product…
Eigenvalue Distribution of -adic Random Matrices Among Algebraic Extensions, with an Analogue for -adic Random Polynomials
Jiahe Shen
We study the distribution of eigenvalues of Haar-random matrices over among algebraic extensions of . Our results give -adic analogues of the real-e…
The Cutoff Profile for Random Transpositions on Repeated Cards in the Full Range of Parameters
Jiahe Shen
The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Be…
The -cycle shuffling with repeated cards
Jiahe Shen
We investigate the -cycle shuffle on repeated cards, namely on a deck consisting of identical copies of each of card types, with total size . We establish asymptot…