14 citations · 23 across the 12 of their papers we have counts for
15 papers
Excessive symmetry can preclude cutoff
Eric Ramos, Graham White
For each , let denote the Kneser Graph; that whose vertices are labeled by -element subsets of , and whose edges indicate that the corresponding subsets…
Monotonicity for continuous-time random walks
Russell Lyons, Graham White
Consider continuous-time random walks on Cayley graphs where the rate assigned to each edge depends only on the corresponding generator. We show that the limiting speed is monotone…
Strong stationary times for features of random walks
Graham White
In [4], we examined the use of coupling to obtain bounds on the mixing time of statistics on Markov chains. In the present paper, we consider the same general problem, but using st…
Coupling for features of random walks
Graham White
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obta…
A variation of strong stationary times for random walks with partial symmetries
Graham White
We introduce a variation of strong stationary times for random walks on the symmetric group. Rather than proceed in the usual fashion of accumulating larger and larger blocks of ca…
A strong stationary time for random transpositions
Graham White
We show that the random transposition walk on the symmetric group has cutoff in separation distance at , by constructing a strong stationary time. The co…
Families of Markov chains with compatible symmetric-group actions
Eric Ramos, Graham White
For each , let denote the Kneser Graph; that whose vertices are labeled by -element subsets of , and whose edges indicate that the corresponding subsets…
A Stationary Planar Random Graph with Singular Stationary Dual: Dyadic Lattice Graphs
Russell Lyons, Graham White
Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary…
FI-sets with relations
Eric Ramos, David Speyer, Graham White
Let FI denote the category whose objects are the sets , and whose morphisms are injections. We study functors from the category FI into the category of sets.…
Families of nested graphs with compatible symmetric-group actions
Eric Ramos, Graham White
For fixed positive integers and , the Kneser graph has vertices labeled by -element subsets of and edges between disjoint sets. Keeping f…
The weak Bruhat order for random walks on Coxeter groups
Graham White
We show that for the simple random walk on a Coxeter group generated by the Coxeter generators and identity, the likelihoods of being at any pair of states respect the weak Bruhat…
Shuffling large decks of cards and the Bernoulli-Laplace urn model
Evita Nestoridi, Graham White
In card games, in casino games with multiple decks of cards and in cryptography, one is sometimes faced with the following problem: how can a human (as opposed to a computer) shuff…
Braid moves in commutation classes of the symmetric group
Anne Schilling, Nicolas M. Thiéry, Graham White +1
We prove that the expected number of braid moves in the commutation class of the reduced word for the long…
Variations of the Poincaré series for affine Weyl groups and q-analogues of Chebyshev polynomials
Eric Marberg, Graham White
Let be a Coxeter system and write for its Poincaré series. Lusztig has shown that the quotient is equal to a certain power series , def…
Automorphisms of geometric structures associated to Coxeter groups
Graham White
In this paper, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for…