<div dir="ltr"><font face="arial, sans-serif" style="text-align:center"><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>, 23 de abril, às <b>15h, </b>acontecerá mais um seminário do ciclo SPSP-IME-USP de 2021. As informações e os vídeos dos seminários estão disponíveis 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><div style="text-align:left">O link para o evento segue abaixo e ficará disponível também na página do evento no dia do seminário.</div></font><font face="arial, sans-serif" style="text-align:center"><div style="text-align:left"><br></div></font><font face="arial, sans-serif" style="text-align:center"><div style="text-align:left">Um abraço,</div><div style="text-align:left">Aline Duarte</div></font><div style="font-family:arial,sans-serif">-------------------------------</div><div style="font-family:arial,sans-serif"><br></div><div><b style="font-family:arial,sans-serif"><font color="#0000ff">Seminar on Probability and Stochastic Processes<br></font></b><br><font face="arial, sans-serif">Speaker: </font><span style="box-sizing:border-box;font-variant-ligatures:none;white-space:pre-wrap;color:rgb(0,0,0);font-family:Arial;vertical-align:baseline"><span style="font-weight:700;box-sizing:border-box">Tertuliano Franco</span></span><span style="box-sizing:border-box;font-variant-ligatures:none;white-space:pre-wrap;font-family:Arial;vertical-align:baseline"><span style="font-weight:700;box-sizing:border-box"> </span></span><span style="box-sizing:border-box;color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap;font-family:Arial;vertical-align:baseline"><span style="font-weight:700;box-sizing:border-box"> </span></span><span style="box-sizing:border-box;color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap;font-family:Arial;vertical-align:baseline">- (</span><span style="box-sizing:border-box;font-variant-ligatures:none;white-space:pre-wrap;color:rgb(0,0,0);font-family:Arial;vertical-align:baseline">IM - UFBA</span><span style="box-sizing:border-box;color:rgb(33,33,33);font-variant-ligatures:none;white-space:pre-wrap;font-family:Arial;vertical-align:baseline">)</span><font face="arial, sans-serif"><br><font color="#ff0000">Next Friday, <b>April 23th - 3pm</b></font><br>Live on Google Meets: <a href="https://meet.google.com/ncm-neqz-dut" target="_blank">https://meet.google.com/ncm-neqz-dut</a> <br></font></div><font face="arial, sans-serif" style="text-align:center"><div style="text-align:left">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> <br></div><div style="text-align:left"><br></div><div style="text-align:left"><p dir="ltr" style="line-height:1.6;margin-top:11.25pt;margin-bottom:0pt"><span style="color:rgb(33,33,33);background-color:transparent;font-weight:700;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap">Title</span><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><span style="font-family:Arial;font-variant-ligatures:none;white-space:pre-wrap">The Slow Bond Random Walk and the Snapping Out Brownian Motion.</span></p><p dir="ltr" style="line-height:1.6;margin-top:11.25pt;margin-bottom:0pt"><span style="background-color:transparent;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap"></span></p><p dir="ltr" style="line-height:1.6;margin-top:0pt;margin-bottom:0pt"><span style="color:rgb(33,33,33);background-color:transparent;font-weight:700;font-variant-numeric:normal;font-variant-east-asian:normal;vertical-align:baseline;white-space:pre-wrap">Abstract</span><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><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><span style="font-family:Arial;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">We consider a continuous time symmetric random walk on the integers, </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">whose rates are equal to 1/2 for all bonds, except for the bond </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">of vertices {−1, 0}, which associated rate is given by \alpha n^{-\beta}/2 , where \alpha and \beta </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">are parameters of the model. We prove here a functional central </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">limit theorem for the random walk with a slow bond: if \beta<1, then it con</span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">verges to the usual Brownian motion. If \beta>1, then it converges to the </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">reflected Brownian motion. And at the critical value \beta = 1, it converges to the </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">snapping out Brownian motion (SNOB) of parameter k = 2 \alpha, which is a Brow</span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">nian type-process recently constructed by Lejay (2016). We also provide Berry-Esseen </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">estimates in the dual bounded Lipschitz metric for the weak convergence of </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">one-dimensional distributions, which we believe to be sharp. </span><span style="font-family:Arial;background-color:transparent;font-variant-ligatures:none;text-decoration-line:inherit;white-space:pre-wrap">Talk based on a joint work with D. Erhard and D. Silva.</span></p></div></font></div>