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<span style="color:rgb(0,0,0)"><font size="2"><span style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255);display:inline;float:none">Dear all,</span></font></span><div><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div><span style="color:rgb(0,0,0)"><font size="2">As a part of the series of seminars <i>"<span>Insalate</span><span> </span>di Matematica"</i>, we<span> </span><span>remind</span><span> </span>you that today there is a seminar held by <b>Simone Baldassarri</b> <span></span><span style="word-spacing:1px"><span></span>(Università degli Studi di Firenze</span><span style="word-spacing:1px">)</span>.<br>Moreover, we remind you that the seminar can also be attended<span> </span><u>in presence</u><span> </span>in room 3014 (building U5-Ratio, Università degli Studi di Milano-Bicocca)<span> </span>by prior reservation at the link<span> </span><a href="https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0" target="_blank">https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0</a><br>You will be required to exhibit your green pass at the entrance of the building.<br><br>Here the details:</font></span></div><div style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><div><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div><span style="color:rgb(0,0,0)"><font size="2"><span style="font-family:Montserrat,Tahoma,Meiryo,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:left;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none"><u>Speaker</u>:<span>
<b>Simone Baldassarri </b></span><b style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:1px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">(</b><b><span style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:1px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Università degli Studi di Firenze)</span></b></span></font></span></div><div><span style="color:rgb(0,0,0)"><font size="2"><span style="font-family:Montserrat,Tahoma,Meiryo,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:left;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none"><br></span></font></span></div></div><span style="color:rgb(0,0,0)"></span><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><u>Date and time</u>: <b>10th February 2022, 2:00 pm (CET)</b></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><u><br></u></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><u>Title</u>: <i style="background-color:rgb(241,194,50)">"Metastability in a lattice gas with strong anisotropic interactions under Kawasaki dynamics</i><span style="background-color:rgb(241,194,50)"><i>"</i></span><i><br><span style="background-color:rgb(241,194,50)"></span></i></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><u>Webex</u>: <a href="https://unimib.webex.com/unimib/j.php?MTID=m1b12166474424f0472cba19aa6190715" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=m1b12166474424f0472cba19aa6190715</a></font></span><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">(<i><u>Password</u></i>: Insalate)</font></span></div>
</div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div dir="ltr"><span style="color:rgb(0,0,0)"><font size="2"><u style="word-spacing:1px">Abstract</u><span style="word-spacing:1px">:
In this talk we will consider
mathematical models evolving according to a stochastic dynamics in order
to identify dynamical properties of real-life systems in the framework
of non-equilibrium statistical mechanics. We will consider a specific
problem in the general study of transitions from local minima to a
global minimum, where the evolution is given by a Markov process. In
particular, we analyze metastability in the context of a local version
of the Kawasaki dynamics for the two-dimensional strongly anisotropic
Ising lattice gas at very low temperature. Let
<img alt="\Lambda\subset\mathbb{Z}^2" title="\Lambda\subset\mathbb{Z}^2" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5CLambda%5Csubset%5Cmathbb%7BZ%7D%5E2" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.5143150345892196" style="display:inline;vertical-align:-0.667px" width="49" height="13"> be a finite box. Particles perform simple
exclusion on <img alt="\Lambda" title="\Lambda" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5CLambda" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.3462954632557844" style="display:inline" width="10" height="11">, but when they occupy neighboring sites they feel
a binding energy <img alt="-U_1<0" title="-U_1<0" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=-U%5F1%3C0" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.5797808539939429" style="display:inline;vertical-align:-2.667px" width="58" height="13"> in the horizontal direction and
<img alt="-U_2<0" title="-U_2<0" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=-U%5F2%3C0" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.3684138742290499" style="display:inline;vertical-align:-2.667px" width="58" height="13"> in the vertical one. Along each bond touching the boundary
of <img alt="\Lambda" title="\Lambda" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5CLambda" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.41649504035710505" style="display:inline" width="10" height="11"> from the outside to the inside, particles are created with
rate <img alt="\rho=e^{-\Delta\beta}" title="\rho=e^{-\Delta\beta}" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Crho=e%5E%7B-%5CDelta%5Cbeta%7D" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.2695158050370521" style="display:inline;vertical-align:-4px" width="62" height="17">, while along each bond from the inside to
the outside, particles are annihilated with rate <img alt="1" title="1" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=1" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.5052564125485504" style="display:inline" width="5" height="10">, where <img alt="\beta" title="\beta" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Cbeta" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.24353743355090263" style="display:inline;vertical-align:-3.333px" width="9" height="14"> is
the inverse temperature and <img alt="\Delta>0" title="\Delta>0" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5CDelta%3E0" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.6270935682285332" style="display:inline;vertical-align:-0.667px" width="42" height="12"> is an activity parameter. We
consider the parameter regime <img alt="U_1>2U_2" title="U_1>2U_2" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=U%5F1%3E2U%5F2" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.9829608027103995" style="display:inline;vertical-align:-2.667px" width="62" height="13"> also known as the strongly
anisotropic regime. We take <img alt="\Delta\in{(U_1,U_1+U_2)}" title="\Delta\in{(U_1,U_1+U_2)}" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5CDelta%5Cin%7B(U%5F1,U%5F1%2BU%5F2)%7D" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.17591934936948506" style="display:inline;vertical-align:-4.333px" width="124" height="16"> and we prove that
the empty (resp. full) configuration is a metastable (resp. stable)
configuration. We consider the asymptotic regime corresponding to finite
volume in the limit of large inverse temperature <img alt="\beta" title="\beta" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Cbeta" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.9846818646149864" style="display:inline;vertical-align:-3.333px" width="9" height="14">. We
investigate how the transition from empty to full takes place. In
particular, we estimate in probability, expectation and distribution the
asymptotic transition time from the metastable configuration to the
stable configuration. Moreover, we identify the size of the critical
droplets, as well as some of their properties. We observe very different
behavior in the weakly (<img alt="U_1<2U_2" title="U_1<2U_2" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=U%5F1%3C2U%5F2" id="m_3311944911517564386m_4069104312381039943gmail-m_-8129548098052925185m_-6026760821752837690m_-923169655236043630gmail-l0.31074662439720546" style="display:inline;vertical-align:-2.667px" width="62" height="13">) and strongly anisotropic
regimes. This is based on a joint work with F. R. Nardi.
</span></font></span>
</div><div dir="ltr"><span style="color:rgb(0,0,0)"><font size="2"><span style="font-family:Roboto,-apple-system,BlinkMacSystemFont,"Apple Color Emoji","Helvetica Neue",sans-serif"><br></span></font></span></div><div dir="ltr"><div dir="auto"><span style="color:rgb(0,0,0)"><font size="2"><u style="word-spacing:1px">Keywords</u><span style="word-spacing:1px">: </span><span style="font-family:Roboto,-apple-system,BlinkMacSystemFont,"Apple Color Emoji","Helvetica Neue",sans-serif"></span>
Metastability - lattice gas - Kawasaki dynamics - critical droplet
</font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div>
<div style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial;background-color:rgb(255,255,255)"><div><span style="color:rgb(0,0,0)"><font size="2"><span><span><div dir="auto"><i><b>** We inform you that the talk will be recorded and uploaded on our website. If you join the talk <u>after the starting time</u>, we kindly ask you to ensure that <u>your microphone and webcam are turned off</u> **</b></i><br></div></span></span></font></span></div><span style="color:rgb(0,0,0)"><font size="2"><span><span><div><br></div><div>We are looking forward to seeing you!<div dir="auto" style="word-spacing:1px"><br></div><div dir="auto" style="word-spacing:1px">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at<span> </span><a href="mailto:insalate.matematica@unimib.it" target="_blank">insalate.matematica@unimib.it</a>.</div><div dir="auto" style="word-spacing:1px"><br></div><div dir="auto" style="word-spacing:1px"><br>The organizers: Luigi Appolloni, Andrea Bisterzo, Alberto Cassella, Francesca Cottini, Ludovico Marini</div></div></span></span></font></span></div></div>
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