10 citations · 47 across the 16 of their papers we have counts for
11 papers · 1 filter
Boundary current fluctuations for the half space ASEP and six vertex model
Jimmy He
We study fluctuations of the current at the boundary for the half space asymmetric simple exclusion process (ASEP) and the height function of the half space six vertex model at the…
Shift invariance of half space integrable models
Jimmy He
We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the color…
Universality for low degree factors of random polynomials over finite fields
Jimmy He, Huy Tuan Pham, Max Wenqiang Xu
We show that the counts of low degree irreducible factors of a random polynomial over with independent but non-uniform coefficients behave like that of a uniform…
Cycles in Mallows random permutations
Jimmy He, Tobias Müller, Teun Verstraaten
We study cycle counts in permutations of drawn at random according to the Mallows distribution. Under this distribution, each permutation is selected with pr…
A central limit theorem for cycles of Mallows permutations
Jimmy He
Fix , and sample from the Mallows measure. We study the distribution of , the number of -cycles, as grows large. When , they are jointly Gau…
Card guessing and the birthday problem for sampling without replacement
Jimmy He, Andrea Ottolini
Consider a uniformly random deck consisting of cards labelled by numbers from through , possibly with repeats. A guesser guesses the top card, after which it is revealed and…
Mixing time of fractional random walk on finite fields
Jimmy He, Huy Tuan Pham, Max Wenqiang Xu
We study a random walk on defined by if , and if , where are inde…
Markov chains on finite fields with deterministic jumps
Jimmy He
We study the Markov chain on obtained by applying a function and adding with equal probability. When is a linear function, this is the well-studied Ch…
The square and add Markov chain
Persi Diaconis, Jimmy He, I. Martin Isaacs
Squaring and adding mod p generates a curiously intractable random walk. A similar process over the finite field (with ) leads to novel connections be…
A central limit theorem for descents of a Mallows permutation and its inverse
Jimmy He
This paper studies the asymptotic distribution of descents $\des(w)$ in a permutation , and its inverse, distributed according to the Mallows measure. The Mallows measure is a n…
Random walk on the symplectic forms over a finite field
Jimmy He
Random transvections generate a walk on the space of symplectic forms on . The main result is establishing cutoff for this Markov chain. After steps, the w…