<div dir="ltr"><font face="arial, sans-serif"><div style="text-align:center"><font face="arial, sans-serif"><div style="text-align:left"><font color="#000000">Caros colegas,</font></div><div style="text-align:left"><font color="#000000"><br></font></div><div style="text-align:left">na próxima <b>sexta-feira</b>, 16 de outubro, às <b>15h, </b>acontecerá mais um seminário do ciclo SPSP-IME-USP. O cronograma dos seminários pode ser acompanhado em  <a href="https://sites.google.com/usp.br/psps-ime-usp" target="_blank">https://sites.google.com/usp.br/psps-ime-usp</a>.</div></font><font face="arial, sans-serif"><div style="text-align:left"><br></div></font><font face="arial, sans-serif"><div style="text-align:left">Um abraço,</div><div style="text-align:left">Aline Duarte</div></font></div><div style="font-size:large">-------------------------------------</div><div style="font-size:large;text-align:center"><br></div><div style="text-align:center;font-size:large"><span style="font-size:small"><font size="4" color="#0000ff"><b>Seminar on Probability and Stochastic Processes</b></font></span></div><div style="text-align:center;font-size:large"><span style="box-sizing:border-box;color:rgb(33,33,33);font-size:17.3333px;font-variant-ligatures:none;white-space:pre-wrap"><span style="font-weight:700;box-sizing:border-box"><br></span></span></div><div style="text-align:center;font-size:large"><span style="color:rgb(33,33,33);font-size:17.3333px;font-variant-ligatures:none;text-align:start;white-space:pre-wrap"> </span><span style="font-variant-numeric:normal;font-variant-east-asian:normal;font-size:13pt;color:rgb(33,33,33);background-color:transparent;vertical-align:baseline;white-space:pre-wrap"> </span><span style="box-sizing:border-box;color:rgb(33,33,33);font-size:17.3333px;font-variant-ligatures:none;white-space:pre-wrap"><span style="font-weight:700;box-sizing:border-box">Dirk Erhard</span></span><span style="color:rgb(33,33,33);font-size:17.3333px;font-variant-ligatures:none;white-space:pre-wrap"> - (IME - UFBA)</span><br></div></font><font face="arial, sans-serif"><div style="text-align:center;font-size:large"><span style="background-color:transparent;font-size:small;white-space:pre-wrap;color:rgb(204,0,0)">Next Friday, October 16th - </span><b style="background-color:transparent;font-size:small;white-space:pre-wrap;color:rgb(204,0,0)">3pm</b></div></font><div><div style="text-align:center"><font face="arial, sans-serif"><span style="color:rgb(33,33,33);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap">Live on Google Meets: </span><a href="https://meet.google.com/htw-ctsn-uua" target="_blank">https://meet.google.com/htw-ctsn-uua</a></font></div><div style="text-align:center"><font face="arial, sans-serif">Video recording will be available on: <a href="https://sites.google.com/usp.br/psps-ime-usp" target="_blank">https://sites.google.com/usp.br/psps-ime-usp</a></font></div><div><font face="arial, sans-serif"><br></font></div><div style="text-align:center"><font face="arial, sans-serif"><br></font></div><div><font face="arial, sans-serif"><span style="color:rgb(33,33,33);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap"><span style="background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline"><b>Title</b>: </span></span><span style="color:rgb(33,33,33);font-size:17.3333px;font-variant-ligatures:none;white-space:pre-wrap"> </span><span style="box-sizing:border-box;color:rgb(33,33,33);font-size:13pt;font-variant-ligatures:none;white-space:pre-wrap;vertical-align:baseline">2D anisotropic KPZ at stationarity</span></font></div><div><span style="color:rgb(33,33,33);background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap"><span style="background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline"><font face="arial, sans-serif"><p dir="ltr" style="line-height:1.6;margin-top:0pt;margin-bottom:0pt"><span style="background-color:transparent;font-weight:700;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline">Abstract</span><span style="background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline">: </span><span style="background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;color:rgb(0,0,0);vertical-align:baseline"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">The KPZ equation is the stochastic partial differential equation in d space dimensions formally given by</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">\partial_t h=\Delta h +\langle h,Q h\rangle +\xi,</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">where \xi is the so called space time white noise, i.e., a gaussian process with short range correlations, and Q is a d</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">dimensional matrix. This equation was introduced in the physics literature in the late eighties to model stochastic growth</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">phenomena, is moreover connected to (d+1) dimensional directed polymers in a random potential and is supposed to arise </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">as a scaling limit of a large class of interacting particle systems.</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">In this talk I will try to explain where this equation comes from, why it is interesting, and how its behaviour depends on the spatial</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">dimension. I will mostly focus on the case of dimension 2, and I will comment on a recent result which contradicts a folklore belief</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit;box-sizing:border-box;vertical-align:baseline">from the physics literature.</span><span style="font-size:13pt;font-variant-ligatures:none;text-decoration-line:inherit"> </span></p></font></span></span><p dir="ltr" class="gmail-CDt4Ke gmail-zfr3Q" style="box-sizing:border-box;font-variant-ligatures:none;margin:15px 0px 0px;outline:none;color:rgb(33,33,33);font-size:13pt;text-decoration-line:inherit;line-height:1.6;white-space:pre-wrap"><span style="box-sizing:border-box;font-size:13pt;vertical-align:baseline"><font face="arial, sans-serif">This is based on joint works with Giuseppe Cannizzaro, Philipp Schönbauer and Fabio Toninelli</font></span></p></div></div></div>