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<p class="p1"><i><span style="font-size:12.0pt;color:#C00000">UNIVERSITY OF CHICAGO</span></i><o:p></o:p></p>
<p class="p1"><i><span style="font-size:12.0pt;color:#C00000">COMPUTER SCIENCE DEPARTMENT</span></i><o:p></o:p></p>
<p class="p1"><i><span style="font-size:12.0pt;color:#C00000">PRESENTS</span></i><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;font-family:Helvetica;color:black">Nguyen Thuy Duong Vuong</span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:Helvetica">Stanford University</span></b><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt">Tuesday, April 19, 2022 at 3:30pm</span></b><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;background:yellow;mso-highlight:yellow">Kent Chemical Laboratory, Room 107</span></b><o:p></o:p></p>
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<p class="MsoNormal" align="center" style="text-align:center;background:white"><b><span style="font-size:12.0pt;font-family:"Open Sans",sans-serif;color:#333333">“Entropic Independence: Optimal Mixing of Local Random Walks”<o:p></o:p></span></b></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span><i><span style="color:black">Abstract:
</span></i><span style="font-size:12.0pt;color:#333333">"In this talk, we will define a notion called entropic independence that is an entropic analog of spectral notions of high dimensional expansion. Informally, entropic independence of a background distribution
µ on k-sized subsets of a ground set of elements says that for any (possibly randomly chosen) set S, the relative entropy of a single element of S drawn uniformly at random carries at most O(1/k) fraction of the relative entropy of S, a constant multiple of
its “share of entropy.” Entropic independence is the natural analog of the recently established notion of spectral independence, if one replaces variance by entropy. Similar to how spectral independence is used to establish lower bounds on the Poincare constant
of certain local random walks, we show a general way to derive lower bounds on the modified log Sobolev constant of these random walks using entropic independence.<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:#333333">Our main applications include tight mixing time bounds for Glauber dynamics on using models whose interaction matrix has eigen spectrum lying within an interval of length
smaller than 1, and for a variation of the Glauber dynamics to sample from the hardcore model on general graphs up to the tree-uniqueness threshold. These results give a quadratic improvement over previously best bounds on the mixing time of these random walks.<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:#333333">Based on joint work with Nima Anari, Vishesh Jain, Frederic Koehler, and Huy Tuan Pham. To appear at STOC 2022.<o:p></o:p></span></p>
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<p class="MsoNormal"><i><span style="font-size:12.0pt;color:black">Bio:</span></i><span style="font-size:12.0pt;color:black"> NguyenThuy-Duong "June" Vuong is a third year PhD student at Stanford University, working with Nima Anari and Moses Charikar. She works
on geometry of polynomials, with applications in sampling and optimization algorithms over combinatorial domain.</span><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;font-family:Helvetica">Host:
</span></b><b><span style="font-size:14.0pt">Madhur Tulsiani</span></b><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-- </span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif">Jose J Fragoso</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif">Project Assistant IV</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif">Computer Science Department</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif">5730 S. Ellis – Room 200C</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif">Chicago, IL. 60637</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif">jfragoso@uchicago.edu</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif">(773) 702-6614</span><o:p></o:p></p>
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