# Analysis and Probability on Infinite-Dimensional Spaces

@article{Eldredge2016AnalysisAP, title={Analysis and Probability on Infinite-Dimensional Spaces}, author={Nathaniel Eldredge}, journal={arXiv: Probability}, year={2016} }

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 Banach spaces. They originated as the notes for a topics course at Cornell University in 2011.

## 16 Citations

### The Gaussian limit for high-dimensional spherical means

- MathematicsJournal of Functional Analysis
- 2019

### Integration on the Hilbert Cube

- Mathematics
- 2017

The aim of this article is to generalize the Lebesgue integration theory to $\mathbb{R}^{\mathbb{N}}$ within a preliminary measure theory, just as an extension of finite dimensional Lebesgue…

### Differential Topology of Gaussian Random Fields

- Mathematics
- 2019

Motivated by numerous questions in random geometry, given a smooth manifold $M$, we approach a systematic study of the differential topology of Gaussian Random Fields (GRF) $X:M\to \mathbb{R}^k$,…

### Evolution of mixed strategies in monotone games

- Economics
- 2022

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time ﬂows which converge in an averaged sense to Nash equilibria. We…

### Quantum Field Theory and Functional Integrals.

- Physics
- 2019

These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's…

### Coupling of Brownian motions in Banach spaces

- Mathematics
- 2017

Consider a separable Banach space $ \mathcal{W}$ supporting a non-trivial Gaussian measure $\mu$. The following is an immediate consequence of the theory of Gaussian measure on Banach spaces: there…

### Diffusion Generative Models in Infinite Dimensions

- Computer ScienceArXiv
- 2022

This work generalizes diffusion models to operate directly in function space by developing the foundational theory for such models in terms of Gaussian measures on Hilbert spaces and developing methods for diffusion generative modeling in Sobolev spaces.

### Fundamental Limitations of Control and Filtering in Continuous-Time Systems: An Information-Theoretic Analysis

- MathematicsArXiv
- 2022

The traditional information-theoretic methods are lifted to infinite-dimensional spaces and formulate various control and filtering systems uniformly as noisy communication channels and the general trade-offs are computed by resorting to the Stratonovich-Kushner equation.

### Variational Inference for Gaussian Process Models with Linear Complexity

- Computer ScienceNIPS
- 2017

A novel variational Gaussian process model that decouples the representation of mean and covariance functions in reproducing kernel Hilbert space is proposed and it is shown that this new parametrization generalizes previous models and makes the adoption of large-scale expressiveGaussian process models possible.

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The classical descriptive set theory is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.