Zobrazeno 1 - 10
of 107
pro vyhledávání: '"He, Jimmy"'
Autor:
He, Jimmy, Wheeler, Michael
We study the periodic $q$-Whittaker and Hall-Littlewood processes, two probability measures on sequences of partitions. We prove that a certain observable of the periodic $q$-Whittaker process exhibits a $(q,u)$ symmetry after a random shift, general
Externí odkaz:
http://arxiv.org/abs/2310.03527
Autor:
He, Jimmy, Schmid, Dominik
We study the speed of convergence to equilibrium for the asymmetric simple exclusion process (ASEP) on a finite interval with one open boundary. We provide sharp estimates on the total-variation distance from equilibrium and verify that the limit pro
Externí odkaz:
http://arxiv.org/abs/2307.14941
Autor:
He, Jimmy
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 boundary at large times. We establish a phase transition depending on
Externí odkaz:
http://arxiv.org/abs/2303.16335
Autor:
He, Jimmy
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 colored stochastic six vertex model in a half space, from which we obtain r
Externí odkaz:
http://arxiv.org/abs/2205.13029
We study cycle counts in permutations of $1,\dots,n$ drawn at random according to the Mallows distribution. Under this distribution, each permutation $\pi \in S_n$ is selected with probability proportional to $q^{\text{inv}(\pi)}$, where $q>0$ is a p
Externí odkaz:
http://arxiv.org/abs/2201.11610
We show that the counts of low degree irreducible factors of a random polynomial $f$ over $\mathbb{F}_q$ with independent but non-uniform coefficients behave like that of a uniform random polynomial, exhibiting a form of universality for random polyn
Externí odkaz:
http://arxiv.org/abs/2201.06156
Autor:
He, Jimmy
Fix $q\neq 1$, and sample $w\in S_n$ from the Mallows measure. We study the distribution of $C_i(w)$, the number of $i$-cycles, as $n$ grows large. When $q<1$, they are jointly Gaussian, and this more or less follows from known ideas, but the regime
Externí odkaz:
http://arxiv.org/abs/2112.09789
Autor:
He, Jimmy, Ottolini, Andrea
Consider a uniformly random deck consisting of cards labelled by numbers from $1$ through $n$, possibly with repeats. A guesser guesses the top card, after which it is revealed and removed and the game continues. What is the expected number of correc
Externí odkaz:
http://arxiv.org/abs/2108.07355
We study a random walk on $\mathbb{F}_p$ defined by $X_{n+1}=1/X_n+\varepsilon_{n+1}$ if $X_n\neq 0$, and $X_{n+1}=\varepsilon_{n+1}$ if $X_n=0$, where $\varepsilon_{n+1}$ are independent and identically distributed. This can be seen as a non-linear
Externí odkaz:
http://arxiv.org/abs/2102.02781
Autor:
He, Jimmy
We study the Markov chain on $\mathbf{F}_p$ obtained by applying a function $f$ and adding $\pm\gamma$ with equal probability. When $f$ is a linear function, this is the well-studied Chung--Diaconis--Graham process. We consider two cases: when $f$ is
Externí odkaz:
http://arxiv.org/abs/2010.10668