@InProceedings{liu:LIPIcs.APPROX/RANDOM.2021.32, author = {Liu, Kuikui}, title = {{From Coupling to Spectral Independence and Blackbox Comparison with the Down-Up Walk}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)}, pages = {32:1--32:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-207-5}, ISSN = {1868-8969}, year = {2021}, volume = {207}, editor = {Wootters, Mary and Sanit\`{a}, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.32}, URN = {urn:nbn:de:0030-drops-147259}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2021.32}, annote = {Keywords: Markov chains, Approximate counting, Spectral independence} }