<div dir="ltr">PROXIMO ENCUENTRO: Miércoles 19 de Junio, 12:00hs.<br><div class="gmail_extra"><div class="gmail_quote"><div><br></div><div><span style="font-family:arial,sans-serif;font-size:13px">EXPOSITOR: Achilleas Tzioufias</span></div>
<div><br></div><div><span style="font-family:arial,sans-serif;font-size:13px">TITULO: </span><span style="font-family:arial,sans-serif;font-size:13px">Proofs from First Principles: An illustrated guide for Contact Processes.</span><span style="font-family:arial,sans-serif;font-size:13px"> </span></div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div dir="ltr">
<div><span style="font-size:13px;font-family:arial,sans-serif"></span></div></div></blockquote><div> </div><div><span style="font-size:13px;font-family:arial,sans-serif">LUGAR: Departamento de Matemática, Aula de</span><span style="font-size:13px;font-family:arial,sans-serif"> seminarios</span><span style="font-size:13px;font-family:arial,sans-serif">, 2do piso, Pabellón 1.</span><br>
</div><div> </div><div><span style="font-family:arial,sans-serif;font-size:13px">RESUMEN:</span></div><div><div style="font-family:arial,sans-serif;font-size:13px">A simple, but somewhat tricky, coupling argument establishes the existence of the decendancy barriers, proposed by <span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">Andjel, E., Mountford, T., Pimentel, L. P., & Valesin, D. (2010). [Tightness for the interface of the one-dimensional contact process. </span><i style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">Bernoulli</i><span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">, </span><i style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">16</i><span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">(4).] for addressing an earlier question of Cox and Durrett (1996), merely on the premises of the celebrated shape theorem. </span><span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">The result is thus extended here to $Z^{D}$, as well as to non-symmetric processes via the work of B</span><font face="Arial, sans-serif"><span style="font-size:12.666666984558105px;line-height:14.541666984558105px">ezuidenhout and G</span></font><span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">ray (1994). Furthermore, a closely related coupling</span> will be<span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px"> shown to suffice for deducing the i.i.d behavior of the endmost points of the 1-D Non-Basic Contact Processes from first principles, while the corresponding result for the Cardinal of the (even basic) process remains a far fetching open problem since Harris' (1974) proof of the Law of Large Numbers for this quantity. </span></div>
<div style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px"><br></span></div><div style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:Arial,sans-serif;font-size:12.727272033691406px;line-height:14.545454025268555px">The analogous to the "tightness for the interface" notion for the contact process in </span><span style="font-family:Arial,sans-serif;font-size:12.666666984558105px;line-height:14.541666984558105px">$d >1$ remains also a related</span><span style="font-family:Arial,sans-serif;font-size:12.666666984558105px;line-height:14.541666984558105px"> open issue which, in the light of our current investigations, is possibly traceable, while contributions in this regard will also be sought from the audience in discussion. </span></div>
<div style="font-family:arial,sans-serif;font-size:13px"><br></div><div style="font-family:arial,sans-serif;font-size:13px">The talk is hybrid: slides on, and proofs by chalk. It also prerequisites familiarity with no more than the Exponential distribution and the Markov property, while, unlike its media res abstract, is given in first things first fashion. </div>
</div></div></div></div>