[Todos] Seminario de Probabilidad

[Matthieu Jonckheere]

PROXIMO ENCUENTRO: Miércoles 19 de Junio, 12:00hs.

EXPOSITOR: Achilleas Tzioufias

TITULO: Proofs from First Principles: An illustrated guide for Contact
Processes.

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LUGAR: Departamento de Matemática, Aula de seminarios, 2do piso, Pabellón 1.

RESUMEN:
A simple, but somewhat tricky, coupling argument establishes the existence
of the decendancy barriers, proposed by Andjel, E., Mountford, T.,
Pimentel, L. P., & Valesin, D. (2010). [Tightness for the interface of the
one-dimensional contact process. *Bernoulli*, *16*(4).] for addressing an
earlier question of Cox and Durrett (1996), merely on the premises of the
celebrated shape theorem. The result is thus extended here to $Z^{D}$, as
well as to non-symmetric processes via the work of Bezuidenhout and Gray
(1994). Furthermore, a closely related coupling will be 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.

The analogous to the "tightness for the interface" notion for the contact
process in $d >1$ remains also a related 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.

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.
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