<div dir="ltr"><div class="gmail_quote"><div dir="ltr"><br><div><p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><b><span lang="EN-US" style="font-size:12pt;line-height:115%">Probability Webinar - IM-UFRJ </span></b></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><b><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Dear colleagues,
</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Our next
online seminar will be held on Monday, <b>September
6, </b> from <b>3 p.m. to 4 p.m</b>. (Rio
de Janeiro local time).</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">The Zoom link for the seminar is </span><span lang="EN-US"></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><a href="https://us02web.zoom.us/j/83698166702?pwd=ejFxYmh3dVk5b3J3SG0wMWxEVnVrUT09" style="color:blue" target="_blank"><span lang="EN-US" style="font-family:Arial,sans-serif;color:rgb(17,85,204);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">https://us02web.zoom.us/j/83698166702?pwd=ejFxYmh3dVk5b3J3SG0wMWxEVnVrUT09</span></a><span lang="EN-US"></span></p><p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><br></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Speaker: <b>Aernout
van Enter (Groningen University)</b></span></p>
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<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Title:
</span><b><span lang="EN-US">Dyson models with random boundary conditions</span></b><span lang="EN-US"></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Abstract:
</span><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span><span lang="EN-US" style="font-size:12pt;line-height:115%;color:black"> </span><span lang="EN-US" style="color:black">I discuss the low-temperature behaviour of Dyson
models (polynomially decaying long-range Ising models in one dimension) in the
presence of random boundary conditions. As for typical random (i.i.d.) boundary
conditions Chaotic Size Dependence occurs, that is, the pointwise thermodynamic
limit of the finite-volume Gibbs states for increasing volumes does not exist,
but the sequence of states moves between various possible limit points, as a
consequence it makes sense to study distributional limits, the so-called
"metastates" which are measures on the possible limiting Gibbs
measures. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="color:black">The Dyson model is known to have a phase transition
for decay parameters </span><span style="color:black">α</span><span lang="EN-US" style="color:black"> between 1 and
2. We show that the metastate changes character at </span><span style="color:black">α</span><span lang="EN-US" style="color:black"> =3/2. It is dispersed in both cases, but it
changes between being supported on two pure Gibbs measures when </span><span style="color:black">α</span><span lang="EN-US" style="color:black"> is less than 3/2 to being supported on mixtures
thereof when </span><span style="color:black">α</span><span lang="EN-US" style="color:black"> is larger than 3/2.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="color:black">Joint work with Eric Endo and Arnaud Le Ny</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%;color:black"> </span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">All the talks
are held in English. </span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">The videos of
the online seminars are available:</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">2020 - <a href="http://www.dme.ufrj.br/?page_id=2885" target="_blank">http://www.dme.ufrj.br/?page_id=2885</a></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">2021-1 -
<a href="http://www.dme.ufrj.br/?page_id=3027" target="_blank">http://www.dme.ufrj.br/?page_id=3027</a></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">For the second semester, a few days after each meeting
the video should be available at <a href="http://www.dme.ufrj.br/?page_id=3178" target="_blank">http://www.dme.ufrj.br/?page_id=3178</a></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Thanks for circulating this information. </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Sincerely, <br>
Organizers: Guilherme Ost and Maria Eulalia Vares</span></p></div></div>
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