<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>, 30 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="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"><span style="font-weight:700;box-sizing:border-box">Alejandra Rada</span></span><span style="color:rgb(33,33,33);font-size:17.3333px;font-variant-ligatures:none;white-space:pre-wrap"> - (UFABC)</span></div><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 30th - </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="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">Title</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">The role of multiple repetitions on the size of a rumor.</span><br></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" class="gmail-CDt4Ke gmail-zfr3Q" style="box-sizing:border-box;font-variant-ligatures:none;margin:0px;outline:none;font-size:13pt;text-decoration-line:inherit;line-height:1.6;padding-top:0px;padding-left:0px"><span style="box-sizing:border-box"><span style="font-weight:700;box-sizing:border-box">Abstract:</span></span> <span style="box-sizing:border-box;font-size:13pt;vertical-align:baseline">We propose a mathematical model to measure how multiple repetitions may influence the ultimate proportion of the population never hearing a rumor during a given outbreak. The model is a multi-dimensional continuous-time Markov chain that can be seen as a generalization of the Maki--Thompson model for the propagation of a rumor within a homogeneously mixing population. In the well-known basic model, the population is made up of ``spreaders'', ``ignorants'' and ``stiflers'', and any spreader attempts to transmit the rumor to the other individuals via directed contacts. In case the contacted individual is an ignorant, it becomes a spreader, while in the other two cases the initiating spreader turns into a stifler. The process in a finite population will eventually reach an equilibrium situation, where individuals are either stiflers or ignorants. We generalize the model by assuming that each ignorant becomes a spreader only after hearing the rumor a predetermined number of times. We identify and analyze a suitable limiting dynamical system of the model, and we prove limit theorems that characterize the ultimate proportion of individuals in the different classes of the population.</span></p><p dir="ltr" class="gmail-CDt4Ke gmail-zfr3Q" style="box-sizing:border-box;font-variant-ligatures:none;margin:15px 0px 0px;outline:none;font-size:13pt;text-decoration-line:inherit;line-height:1.6;padding-left:0px"><span style="box-sizing:border-box;font-size:13pt;vertical-align:baseline">This is a join work with  Cristian Coletti, Elcio Lebensztayn and  Pablo M. Rodriguez.</span></p></font></span></span></div></div></div>