63 citations · 138 across the 14 of their papers we have counts for
15 papers
A probabilistic look at the infinite hat-guessing game
Nathaniel Eldredge
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of…
Uniform doubling for abelian products with
Nathaniel Eldredge, Maria Gordina, Laurent Saloff-Coste
We prove that the uniform doubling property holds for every Lie group which can be written as a quotient group of for some . In partic…
Notions of null sets in infinite-dimensional Carnot groups
Nathaniel Eldredge, Maria Gordina, Enrico Le Donne +1
We study several notions of null sets on infinite-dimensional Carnot groups. We prove that a set is Aronszajn null if and only if it is null with respect to measures that are convo…
Transportation inequalities for Markov kernels and their applications
Fabrice Baudoin, Nathaniel Eldredge
We study the relationship between functional inequalities for a Markov kernel on a metric space and inequalities of transportation distances on the space of probability measure…
Left-invariant geometries on are uniformly doubling
Nathaniel Eldredge, Maria Gordina, Laurent Saloff-Coste
A classical aspect of Riemannian geometry is the study of estimates that hold uniformly over some class of metrics. The best known examples are eigenvalue bounds under curvature as…
Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups
Nathaniel Eldredge
On a stratified Lie group equipped with hypoelliptic heat kernel measure, we study the behavior of the dilation semigroup on spaces of log-subharmonic functions. We consi…
Analysis and Probability on Infinite-Dimensional Spaces
Nathaniel Eldredge
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Ban…
Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
Nathaniel Eldredge, Leonard Gross, Laurent Saloff-Coste
We show that for a hypoelliptic Dirichlet form operator A on a stratified complex Lie group, if the logarithmic Sobolev inequality holds, then a holomorphic projection of A is stro…
An eigenspace approach to isotypic projections for data on binary trees
Nathaniel Eldredge
The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider…
On complex H-type Lie algebras
Nathaniel Eldredge
H-type Lie algebras were introduced by Kaplan as a class of real Lie algebras generalizing the familiar Heisenberg Lie algebra . The H-type property depends on a ch…
Hypoelliptic heat kernel inequalities on H-type groups
Nathaniel Eldredge
We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the h…
Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups
Bruce K. Driver, Nathaniel Eldredge, Tai Melcher
We study the law of a hypoelliptic Brownian motion on an infinite-dimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can…
Widder's representation theorem for symmetric local Dirichlet spaces
Nathaniel Eldredge, Laurent Saloff-Coste
In classical PDE theory, Widder's theorem gives a representation for nonnegative solutions of the heat equation on . We show that an analogous theorem holds for local…
Gradient estimates for the subelliptic heat kernel on H-type groups
Nathaniel Eldredge
We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups of H-type: where is the heat s…
Precise estimates for the subelliptic heat kernel on H-type groups
Nathaniel Eldredge
We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups of H-type. Specifically, we show that there exist positive constants ,…