##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics

## Chris Gartland

#### UC San Diego

## Stochastic Embeddings of Hyperbolic Metric Spaces

##### Abstract:

This talk is based on ongoing work of the speaker. We will discuss the stochastic embeddability of snowflakes of finite Nagata-dimensional spaces into ultrametric spaces and the induced stochastic embeddings of their hyperbolic fillings into trees. Several results follow as applications, for example:

(1) For any uniformly concave gauge $\omega$, the Wasserstein 1-metric over $([0,1]^n,\omega(\|\cdot\|))$ biLipschitzly embeds into $\ell^1$.

(2) The Wasserstein 1-metric over any finitely generated Gromov hyperbolic group biLipschitzly embeds into $\ell^1$.

### October 5, 2023

### 11:00 AM

APM 6402

Research Areas

Probability Theory****************************