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<p class="MsoNormal"><o:p> </o:p></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:"Arial",sans-serif;color:#286DC0;text-decoration:none"><img border="0" width="150" height="49" style="width:1.5625in;height:.5104in" id="logo" src="cid:image001.jpg@01DBA2FA.ECFC6810" alt="Department of Statistics and Data Science
"></span></a></span><span style="font-size:11.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none">
</span><span style="color:black"><a href="https://statistics.yale.edu/" title="Home"><b><span style="font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none">Department of Statistics and Data Science </span></b></a></span><b><i><u><span style="font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none">
<o:p></o:p></span></u></i></b></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none">Ramon van Handel, Princeton University<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><img border="0" width="162" height="194" style="width:1.6875in;height:2.0208in" id="Picture_x0020_2" src="cid:image002.png@01DBA2FA.ECFC6810"><span style="mso-ligatures:none"><o:p></o:p></span></span></p>
<p class="MsoNormal"><b><u><span style="font-family:"Arial",sans-serif;mso-ligatures:none">Date: Monday, April 07, 2025<o:p></o:p></span></u></b></p>
<p class="MsoNormal"><b><u><span style="font-family:"Arial",sans-serif;mso-ligatures:none">Time: 4:00PM to 5:00PM<o:p></o:p></span></u></b></p>
<p class="MsoNormal"><b><u><span style="font-family:"Arial",sans-serif;mso-ligatures:none">Location: SPL 59 <a href="http://maps.google.com/?q=217+Prospect+Street%2C+New+Haven%2C+CT%2C+06511%2C+us">See map</a> <o:p></o:p></span></u></b></p>
<p class="MsoNormal"><b><u><span style="font-family:"Arial",sans-serif;mso-ligatures:none">217 Prospect Street<o:p></o:p></span></u></b></p>
<p class="MsoNormal"><b><u><span style="font-family:"Arial",sans-serif;mso-ligatures:none">New Haven, CT 06511<o:p></o:p></span></u></b></p>
<p class="MsoNormal"><b><span style="font-family:"Arial",sans-serif;mso-ligatures:none"><a href="https://web.math.princeton.edu/~rvan/">Website</a><o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none">Title: Sharp matrix concentration inequalities<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none">Information and Abstract: <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none">Much of random matrix theory is concerned with a relatively small collection of special random matrix models whose asymptotic behavior can be studied in stunning detail. But
random matrices that arise naturally in other areas of pure and applied mathematics are often not of this form and may admit an essentially arbitrary structure. The main tools that have been used to study such models, known as matrix concentration inequalities,
are extremely general but only provide crude information.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none">In the past few years, however, powerful new tools were discovered to obtain a sharp understanding, to leading order, of the spectral statistics of arbitrarily structured random
matrices under surprisingly minimal assumptions. I will aim to describe how these methods work and explain how they enable the study of new applications, such as phase transition phenomena for nonhomogeneous random matrices, that are fundamentally outside
the reach of traditional matrix concentration inequalities.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none">This talk is based on joint works with A. Bandeira, M. Boedihardjo, T. Brailovskaya, G. Cipolloni, and D. Schroeder.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><u><span style="font-family:"Arial",sans-serif;mso-ligatures:none">3:15pm - Pre-talk meet and greet teatime – Kline Tower, 219 Prospect Street, 13 floor, there will be light snacks and beverages in the kitchen area.<o:p></o:p></span></u></b></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black;mso-ligatures:none">For more details and upcoming events visit our website at
</span><span style="font-family:"Arial",sans-serif"><a href="https://statistics.yale.edu/calendar"><span style="color:#467886;mso-ligatures:none">https://statistics.yale.edu/calendar</span></a><span style="mso-ligatures:none">.
<o:p></o:p></span></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Arial",sans-serif;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:18.0pt;font-family:"Arial",sans-serif;mso-ligatures:none">Department of Statistics and Data Science<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none">Yale University<br>
Kline Tower<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:"Arial",sans-serif;color:black;mso-ligatures:none">219 Prospect Street<br>
New Haven, CT 06511<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><a href="https://statistics.yale.edu/"><span style="color:#467886">https://statistics.yale.edu/</span></a><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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