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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal style='margin-bottom:12.0pt'><u><span style='font-size:14.0pt;color:red'>In-Person seminars will be held at Dunham Lab, 10 Hillhouse Ave., Room 220, with an option of remote participation via zoom.</span><o:p></o:p></u></p><p class=MsoNormal style='background:white'><span style='color:black'><a href="https://statistics.yale.edu/" title="Department of Statistics and Data Science
"><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5069in' id=logo src="cid:image001.jpg@01D8BC86.EA2FA460" alt="Department of Statistics and Data Science
"></span></a> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal style='margin-top:.1in'><span class=date-display-single><i><u><span style='font-size:16.0pt;font-family:"Arial",sans-serif'>We invite you to attend our in-person seminar.</span></u></i></span><span class=date-display-single><span style='font-size:13.0pt;font-family:"Arial",sans-serif;background:white'><o:p></o:p></span></span></p><p class=MsoNormal style='margin-top:.1in'><span style='font-size:16.0pt;font-family:"Arial",sans-serif;color:black;background:white'>Ahmed El Alaoui</span><span style='font-size:13.0pt;font-family:"Arial",sans-serif;color:black;background:white'>, Cornell University</span><o:p></o:p></p><p class=MsoNormal style='background:white'><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></span></p><p class=MsoNormal style='background:white'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=136 height=163 style='width:1.4166in;height:1.6944in' src="cid:image004.jpg@01D8C9BD.300908D0" align=left hspace=12 v:shapes="Picture_x0020_2"><![endif]><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Monday, September 19, 2022</span></span><span class=date-display-single><span style='font-size:12.0pt'><o:p></o:p></span></span></p><p class=MsoNormal style='background:white'><span class=date-display-start><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>5:00PM</span></span><o:p></o:p></p><p class=MsoNormal style='background:white'><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Dunham Lab.</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> </span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>10 Hillhouse Avenue, Rm. 220</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=locality><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>New Haven</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>, <span class=region>CT</span> <span class=postal-code>06511</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=fn><b><i><span style='color:black'>OR</span><o:p></o:p></i></b></span></p><p class=MsoNormal style='background:white'><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Via Zoom:</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> / Password: 24</span><o:p></o:p></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'><a href="https://statistics.yale.edu/seminars/ahmed-el-alaoui">https://statistics.yale.edu/seminars/ahmed-el-alaoui</a></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>Title: Sampling from the SK measure via algorithmic stochastic localization<o:p></o:p></span></b></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Information and Abstract: </span></b><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></b></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-family:"Arial",sans-serif;color:black'>The Sherrington-Kirkpatrick measure is a random probability distribution on the hypercube, which is a central object of study in probability theory and in the mean-field theory of disordered statistical physics models. </span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif;color:black'>In this talk I will present an algorithm which efficiently samples from the SK measure with no external field and at high temperature. The approach uses a discretized version of the stochastic localization process of Eldan, together with a subroutine for computing the mean vector, or magnetization, of a family of SK measures tilted by an appropriate external field. This approach is very general and has wide applicability. </span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Our analysis shows that the algorithm outputs an approximate sample (in a certain weak sense) from the SK measure, for all inverse temperatures beta < 1/2. In a recent paper, Celentano (2022) shows that our algorithm succeeds up to the critical temperature beta < beta_c = 1. </span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif;color:black'>Conversely, we show that in the ‘low temperature’ phase beta >1, no ‘stable’ algorithm can approximately sample from the SK measure. This exploits a newly established strong version of a property called `disorder chaos’ exhibited by SK in this regime. </span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif;color:black'>The above two results settle the question of the computational tractability of sampling from SK for all temperatures except the critical one. </span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p style='margin:0in;background:white'><span style='font-family:"Arial",sans-serif;color:black'>This is based on a <a href="https://arxiv.org/abs/2203.05093"><span style='color:black;text-decoration:none'>joint work</span></a> with Andrea Montanari and Mark Sellke. </span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><i><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></i></p><p class=MsoNormal style='line-height:18.0pt;background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'><a href="x-apple-data-detectors://10/"><span style='color:black;text-decoration:none'>3:30pm</span></a> - Pre-talk meet and greet.</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Zoom Link: </span></b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Via Zoom: Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> </span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> Password: 24<br> Or Telephone</span><span lang=JA style='font-size:12.0pt;font-family:"MS PGothic",sans-serif'>：</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>203-432-9666 (2-ZOOM if on-campus) or 646 568 7788<br> Meeting ID: 924 1107 7917</span><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal style='line-height:18.0pt;background:white'><o:p> </o:p></p><p class=MsoNormal style='background:white;vertical-align:baseline'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>For more details and upcoming events visit our website at <a href="http://statistics.yale.edu/"><span style='color:black'>http://statistics.yale.edu/</span></a> .</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt'><o:p> </o:p></span></p></div></body></html>