endobj 89 0 obj << /S /GoTo /D (subsection.5.1) >> 65 0 obj This book is an introduction to the modern approach to the theory of Markov chains. 0000014564 00000 n << /S /GoTo /D (subsection.2.1) >> << /S /GoTo /D (section.4) >> 20 0 obj stream Math, physics, history, economics, all of these appeared plausible choices which I had some interest in. endobj (Canonical paths) 0000067512 00000 n << /S /GoTo /D (section.3) >> 105 0 obj 0000002221 00000 n >> << /S /GoTo /D (section.5) >> << /S /GoTo /D (subsection.3.3) >> 8 0 obj 0000018258 00000 n endobj << /S /GoTo /D (section.2) >> (Total variation distance and coupling) 0000053681 00000 n 0000008717 00000 n endobj 0000070393 00000 n << << /S /GoTo /D (subsection.2.3) >> 0000033650 00000 n 40 0 obj endobj 93 0 obj endobj (Monotone chains) 0000025145 00000 n 72 0 obj 57 0 obj << /S /GoTo /D (subsection.6.2) >> << /S /GoTo /D (subsection.6.1) >> 0000025638 00000 n 0000068524 00000 n 0000014884 00000 n endobj (Bottleneck ratio) 0000055249 00000 n 0000018311 00000 n %���� 0000065050 00000 n << /S /GoTo /D (subsection.4.2) >> Check that d(t) is a non-increasing function of t. We de ne the mixing time to be the rst time the total variation distance from stationarity drops below ", i.e. 0000017767 00000 n 0000030617 00000 n As we shall see, this is the case for any sequence of vertex-transitive graphs of polynomial growth. 0000066370 00000 n 0000011238 00000 n 68 0 obj stream 37 0 obj 0000040148 00000 n (Random walk on the d-ary tree of depth ) << /S /GoTo /D (subsubsection.2.1.1) >> 1 0 obj << /S /GoTo /D (subsubsection.2.1.2) >> << /S /GoTo /D (subsection.1.3) >> 0000026922 00000 n (Spectral decomposition and relaxation time) endobj 0000012448 00000 n 108 0 obj x�u˒��>_�[����#�d�Yo&�ǖ=�l0"$��$� 9�����$jV{� 4��F?����d��.������w?��*��,-���n�q�4�*k��W�����'�Ō��&O�������x�I��uVE�^��������I=��&��uVG��|�5v�>���U�UV! endobj �'�E�B>1�����]�_��~7��,��}{n�x��S؛��|�. 0000068726 00000 n << /S /GoTo /D (subsection.1.1) >> 53 0 obj 0000026899 00000 n endobj Random walks on graphs Simple random walk on a sequence of graphs. 0000026174 00000 n 101 0 obj << /S /GoTo /D (section.1) >> 0000013379 00000 n 0000053206 00000 n 0000048682 00000 n 0000046806 00000 n �5��nW�z�U6��� �]ϟ�T����y4����9�f6M�1��{�9���V���j*���!vv8��p�h{x��m�m����ls;�-�B[��/#'v�P}-Ň�ST1ׁM��>�W63�˅/2��kS���pc�׼��_7�r ���ڏf�BOm7(��۫��=����aP��۽f�h?qW���xU=��8&�������+�ٵW "�z��m�TyǗ��$ɧ$9������C�����3���=��'�G���r�B��>��;�S�*@�p&�?&��n0��xŔ�/B���u���g�� << /S /GoTo /D (subsection.5.2) >> 97 0 obj 73 0 obj 0000050777 00000 n H��VK�ww�4�k'�{�@E���ʲl_@��*s (U���k/JD�#�c���]?�Z�T�@b�����Y?W*j��"�H�RrC=��Z��of�DE)��3������5&����������o�����y���`�ܗ�����3'"�;���''Il�����E��S��~�������3�k�!�u�e��c��!�Q+��S�����[�� 2 0 obj (Spectral techniques) 0000048209 00000 n 0000017714 00000 n endobj endobj endstream /Length 2509 0000031749 00000 n endobj endobj 0000067994 00000 n 0000040438 00000 n endobj 16 0 obj endobj 0000054599 00000 n 80 0 obj endobj (Comparison technique) endobj 4 0 obj << /S /GoTo /D [114 0 R /Fit] >> Request PDF | On Oct 31, 2017, David Levin and others published Markov Chains and Mixing Times | Find, read and cite all the research you need on ResearchGate 255 0 obj (Dirichlet form and the bottleneck ratio) endobj 12 0 obj Markov Chains, Mixing Times and Coupling Methods with an Application in Social Learning Senior Thesis submitted by Jinming Zhang June 4, 2020 Advisor: Ursula Porod Northwestern University. /First 812 0000025757 00000 n 0000034934 00000 n (Ising model) >> 138 0 obj 0000002111 00000 n %PDF-1.5 81 0 obj (Coupling from the past) endobj 0000012055 00000 n 0000030640 00000 n 44 0 obj 0000018727 00000 n endobj (Markovian coupling and other metrics) 41 0 obj 0000068315 00000 n 48 0 obj 0000040632 00000 n 0000034037 00000 n endobj xڕWMs�6��W�-�:@�d'���I�C�f���LC"b�d ȱ���V$eَDe�4h������PF*!M�����DBB�Q$��DJ��$r�xDA2�#H�j!%,S|!�J��T�a�R@ 2MKLPZ��R�V�i�D`i��$��,#]�j�1��m���,����S)0Tb[-���`Eˆp9���$��%F���(%�K•qI,��J0W�y���S�R0F�e` ��P���ӈ��F�%�4�#�,B�"�B$�b�_ ���'0f5hP����u��)�_�$_X�$�d�Y6П�G�0/������NB)�ɑ� ��[A����E�gl,S�T 9��ȔɄ2�P���$� 9c72� &Ro �� endobj endobj (Path metric) It … << /S /GoTo /D (subsection.3.2) >> 0000011013 00000 n 0000039870 00000 n trailer << /Size 864 /Info 749 0 R /Root 777 0 R /Prev 710079 /ID[<4b68ec8e98c3a020314dd4f4afb2882f><697dcc76edc4c537a22dbff4032ce220>] >> startxref 0 %%EOF 777 0 obj << /Type /Catalog /Pages 762 0 R /Metadata 750 0 R /JT 775 0 R /PageLabels 748 0 R >> endobj 862 0 obj << /S 11356 /T 11740 /L 11931 /Filter /FlateDecode /Length 863 0 R >> stream