MARC details
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02842ntm a22003137a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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AT-ISTA |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20250915095143.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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250915s2024 au ||||| m||| 00| 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Transcribing agency |
ISTA |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Pedrotti, Francesco |
| 9 (RLIN) |
1084221 |
| 245 ## - TITLE STATEMENT |
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| Title |
Functional inequalities and convergence of stochastic processes |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc. |
Institute of Science and Technology Austria |
| Date of publication, distribution, etc. |
2024 |
| 500 ## - GENERAL NOTE |
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| General note |
Thesis |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Abstract |
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Acknowledgements |
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About the Author |
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List of Collaborators and Publications |
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Table of Contents |
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| Formatted contents note |
1 Introduction |
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2 Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces |
| 505 ## - FORMATTED CONTENTS NOTE |
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3 Contractive coupling rates and curvature lower bounds for Markov chains |
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4 Improved Convergence of Score-Based Diffusion Models via Prediction-Correction |
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5 Heat flow, log-concavity, and Lipschitz transport maps |
| 505 ## - FORMATTED CONTENTS NOTE |
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6 L^∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model<br/> |
| 505 ## - FORMATTED CONTENTS NOTE |
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Bibliography |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This thesis deals with the study of stochastic processes and their ergodicity properties. The variety of problems encountered calls for a set of different approaches, ranging from classical to modern ones: a special place is held by probabilistic methods based on couplings, by functional inequalities, and by the theory of gradient flows in the space of measures. The material is organized as follows. Chapter 1 contains the introduction to this thesis, starting with a general presentation of some of the relevant topics. Section 1.1 is dedicated to the theory of gradient flows in metric spaces, and introduces the first contribution of this thesis [DSMP24], which is presented in detail in Chapter 2. Section 1.2 moves to the topic of curvature of Markov chains, concluding with a brief description of our second contribution [Ped23], which is included in Chapter 3. Section 1.3 discusses applications of stochastic processes to the theory of sampling, in particular the recent framework of score-based diffusion models, and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses some related problems, concerning the regularization properties of the heat flow. It serves as a motivation for the work [BP24], which we report in Chapter 5. Finally, Section 1.5 discusses the last contribution of this thesis, which can be found in Chapter 6. It deals with the convergence to equilibrium of a particular stochastic model from quantitative genetics: this is established via some functional inequalities, which we prove with probabilistic arguments based on couplings. |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.15479/at:ista:17336">https://doi.org/10.15479/at:ista:17336</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |