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<div dir="ltr"><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">As part of the series of seminars <i>"Insalate di Matematica"</i>, <b>Simone Baldassarri</b>, PhD student at <span style="word-spacing:0px">the Università degli Studi di Firenze</span><font style="word-spacing:0px"><span style="word-spacing:1px">, will deliver a talk. </span></font></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">According to the current Covid regulations, the seminar will be held in a <u>hybrid mode</u> <b>(more information below)</b>.</font></span></div><div 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">Here the details:</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"><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 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_-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_-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_-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_-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_-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_-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_-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_-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_-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_-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_-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_-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_-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="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><b><u>Information to attend in room 3014<br></u></b></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">The
seminar will take place in room 3014, at the building U5-Ratio,
Università degli Studi di Milano Bicocca. Unfortunately, only a limited
number of participants is allowed in presence, hence reservation is mandatory. You can reserve at the following link: <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> </font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">We also remind that you will be required to exhibit your green pass at the entrance of the building.</font></span></div><div 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"><b><u>Information to attend online</u></b></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">The seminar will be streamed via Webex platform at the following link: <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><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">(<i><u>Password</u></i>: Insalate)<br></font></span></div><div dir="auto"><span style="color:rgb(0,0,0)"><font size="2"><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></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">You can find the poster of the event in the attachment. We are looking forward to seeing you! </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">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 <a href="mailto:insalate.matematica@unimib.it" target="_blank">insalate.matematica@unimib.it</a>.</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>The organizers: Luigi Appolloni, Andrea Bisterzo, Alberto Cassella, Francesca Cottini, Ludovico Marini</font></span></div></div></div>
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