Bob Hough

activity

20102016

most citedMixing and cut-off in cycle walks

12 citations · 16 across the 2 of their papers we have counts for

collaborators

10 papers

math.NT2016★ 4 cited

Maass form twisted Shintani $L$ -functions

Bob Hough

The Maass-form twisted Shintani $L$ -functions are introduced, and some of their analytic properties are studied. These functions contain data regarding the distribution o…

math.PR2016

The random $k$ cycle walk on the symmetric group

Bob Hough

We study the random walk on the symmetric group $S_{n}$ generated by the conjugacy class of cycles of length $k$ . We show that the convergence to uniform measure of this walk has a c…

math.NT2015★ 12 cited

Mixing and cut-off in cycle walks

Bob Hough

Given a sequence $(X_{i}, K_{i})_{i = 1}^{\infty}$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lo…

math.NT2013

Solution of the minimum modulus problem for covering systems

Bob Hough

We answer a question of Erdős by showing that the least modulus of a distinct covering system of congruences is no larger than $1 0^{18}$ .

math.NT2013

The angle of large values of $L$ -functions

Bob Hough

We prove omega results for the central value of $L$ -functions with the further condition that the angle is also constrained.

math.PR2012

Cut-off phenomenon in the uniform plane Kac walk

Bob Hough, Yunjiang Jiang

We consider an analogue of the Kac random walk on the special orthogonal group $S O (N)$ , in which at each step a random rotation is performed in a randomly chosen 2-plane of $\bR^N$…

Maass form twisted Shintani L-functions

The random k cycle walk on the symmetric group

Mixing and cut-off in cycle walks

Solution of the minimum modulus problem for covering systems

The angle of large values of L-functions

Cut-off phenomenon in the uniform plane Kac walk

Maass form twisted Shintani $L$ -functions

The random $k$ cycle walk on the symmetric group

The angle of large values of $L$ -functions