arXiv subjects

Hester Pieters

Publications and source records attributed to Hester Pieters.

4 recordsLinked to original sources

arXiv2022

Community detection and percolation of information in a geometric setting

We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph over a homogeneous metric space where the probability of two vertices to be connected is an arbitrary function of the distance. We give sufficient conditions under which the locations can be recovered (up to an isomorphism of the space) in the sparse regime. Moreover, we define a geometric counterpart of the model of flow of information on trees, due to Mossel and Peres, in which one considers a branching random walk on a sphere and the goal is to recover the location of the root based on the locations of leaves. We give some sufficient conditions for percolation and for non-percolation of information in this model.

stat.ML↗

arXiv2018

The Gromov norm of the quaternionic Kähler class

We prove that the embedding of the quaternionic hyperbolic disc $H^1_\mathbb{H}$ into quaternionic hyperbolic $n$-space $H^n_\mathbb{H}$ is tight and thereby obtain the value of the Gromov norm of the quaternionic Kähler class.

math.GT↗

arXiv2018

New bounds for the simplicial volume of complex hyperbolic surfaces

We give estimates of the Gromov norm of the top dimensional class in $H_c^4(\mathrm{Isom}(\mathbb{H}_{\mathbb{C}}^2);\mathbb{R})$. As a consequence, we obtain an explicit upper bound for the simplicial volume of closed oriented manifolds that are locally isometric to $\mathbb{H}_{\mathbb{C}}^2$.

math.GT↗

arXiv2018

The boundary model for the continuous cohomology of Isom$^+(\mathbb{H}^n)$

We prove that the continuous cohomology of $\text{Isom}^+(\mathbb{H}^n)$ can be measurably realized on the boundary of hyperbolic space. This implies in particular that for $\text{Isom}^+(\mathbb{H}^n)$ the comparison map from continuous bounded cohomology to continuous cohomology is injective in degree $3$. We furthermore prove a stability result for the continuous bounded cohomology of $\text{Isom}(\mathbb{H}^n)$ and $\text{Isom}(\mathbb{H}_{\mathbb{C}}^n)$.

math.GR↗