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In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusApproximate and Exact Solutions of Intertwining Equations Through Random Spanning Forests

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: Approximate and Exact Solutions of... [For different reversible Markov kernels on finite state spaces, we look for families of probability measures for which the time evolution almost remains in their convex hull. Motivated by signal processing problems and metastability studies we are interested in the case when the size of such families is smaller than the size of the state space, and we want such distributions to be with “small overlap” among them. To this aim we introduce a squeezing function to measure the common overlap of such families, and we use random forests to build random approximate solutions of the associated intertwining equations for which we can bound from above the expected values of both squeezing and total variation errors. We also explain how to modify some of these approximate solutions into exact solutions by using those eigenvalues of the associated Laplacian with the largest size.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusApproximate and Exact Solutions of Intertwining Equations Through Random Spanning Forests

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.
Avena, Luca; Castell, Fabienne; Gaudillière, Alexandre; Mélot, Clothilde
In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius — Nov 4, 2020
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References (37)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
27 –69
DOI
10.1007/978-3-030-60754-8_3
Publisher site
See Chapter on Publisher Site

Abstract

[For different reversible Markov kernels on finite state spaces, we look for families of probability measures for which the time evolution almost remains in their convex hull. Motivated by signal processing problems and metastability studies we are interested in the case when the size of such families is smaller than the size of the state space, and we want such distributions to be with “small overlap” among them. To this aim we introduce a squeezing function to measure the common overlap of such families, and we use random forests to build random approximate solutions of the associated intertwining equations for which we can bound from above the expected values of both squeezing and total variation errors. We also explain how to modify some of these approximate solutions into exact solutions by using those eigenvalues of the associated Laplacian with the largest size.]

Published: Nov 4, 2020

Keywords: Intertwining; Markov process; Finite networks; Multiresolution analysis; Metastability; Random spanning forests; 05C81; 15A15; 60J28

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