Title: "Free energy of two-species systems with applications to colloids"
Speaker: Dimitrios Tsagkarogiannis (Università degli Studi dell'Aquila)
Abstract: In this talk we consider a system of small and large spheres in a continuous medium all interacting via positive potentials. This could describe colloidal particles (large spheres) within a substrate (small spheres). Alternatively, it could provide an idealized picture of what may happen in a phase transition when the new phase is getting formed (large spheres) but we still have small isolated particles (small spheres). One interesting phenomenon that occurs is that despite the repulsive forces between all particles, when we look at the effective system of only big spheres there is an attractive force between them usually referred to as "depletion attraction". The question we address in this talk is how to compute the free energy of the system, in particular for the renormalized one, i.e., when we first integrate over the small spheres. We will discuss a sufficient condition for the convergence of the related cluster expansion, which involves the surface of the large spheres rather than their volume (as it would have been the case in a direct application of existing methods to the binary system). This is based on joint works with Sabine Jansen (LMU) as well as with Giuseppe Scola (SISSA) and Xuan Nguyen (NYU-Shanghai).
April 29, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)
Local: This meeting will take place on Google Meet, through the link below:
https://meet.google.com/haf-zcxs-ckx
More complete information about the seminars can be found HERE.
Sincerely,
Organizers: Giulio Iacobelli e Maria Eulalia Vares
Title: "Ramsey numbers"
Speaker: Simon Griffiths (PUC-Rio)
Abstract: We shall discuss recent progress related to Ramsey numbers, and the relation with problems in probability. The talk will be based on joint work with Marcelo Campos, Rob Morris and Julian Sahasrabudhe.
April 8, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)
Local: room B106-a - Bloco B - CT – Instituto de Matemática – UFRJ. There will be no transmission online.
More complete information about the seminars can be found HERE.
Sincerely,
Organizers: Giulio Iacobelli and Maria Eulalia Vares
Probability Seminar “New results for the simple parking process”
March 11, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)
Local: Sala C116, Instituto de Matematica - UFRJ
Speaker: Sandro Gallo (DEs -UFSCar)
Abstract: We consider the parking process on the grid with a simple occupancy scheme, which is defined as follows. Initially, all the sites in Λn := {−n, . . . , n} d are empty. At each step, a site is chosen uniformly at random in Λn and if it and its nearest neighbors are empty, the chosen site is occupied. Once occupied, the site remains so forever. We will discuss the statistical properties of the proportion of occupied sites for this model and for its thermodynamic limit defined on the integer grid Z d . This talk is based on ongoing work in collaboration with Alejandro Roldan (UdeA, Colombia), ´ Alexander Leon (UdeA, Colombia) and Cristian Coletti (UFABC, Brazil)
More complete information about the seminars can be found at DME
Title: "A Central Limit Theorem for intransitive dice"
Speaker: Daniel Ungaretti
Abstract: Consider dice that are allowed to have different numbers of faces and any number on each face. Die A is said to be better than die B, denoted A ▷ B, if it has a larger probability of winning. This ordering of dice is not transitive: it is possible that A ▷ B ▷ C ▷ A. In this talk we present results on the probability of random dice (with i.i.d. faces) forming an intransitive chain, as the number of faces of each die goes to infinity. We prove a Central Limit Theorem for such dice, combining the method of moments with simple graph theory arguments.
March 25, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time).
Local: room C116 - Bloco C - CT – Instituto de Matemática – UFRJ.
More complete information about the seminars can be found HERE.
Sincerely,
Organizers: Giulio Iacobelli and Maria Eulalia Vares
Probability Seminar “Inhomogeneous percolation with random one-dimensional reinforcements”
January 15, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)
Local: room C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.
Speaker: Alan Bruno do Nascimento (UFMG)
Abstract: In this talk we consider inhomogeneous Bernoulli bond percolation on the graph GxZ, where G is an infinite connected graph with bounded degree and Z is the set of integers. In 1994, Madras, Schinazi and Schonman showed that there is no percolation in Z^d if the edges are open with a probability of q<1 if they lie on a fixed axis and with a probability of p<p_c(Z^d) otherwise. Here, we consider a region given by boxes with iid radii centered along the vertical axis 0xZ of GxZ. We allow each edge to be open with a probability of q<1 if it is inside this region and with a probability of p<p_c(GxZ) otherwise. The goal of the talk is to show that, even if the region is connected, occurrence or not of percolation in this inhomogeneous model depends on how sparse and how large are the boxes placed along the axis. We aim to give sufficient conditions on the moments of the radii as a function of the growth of the graph G for percolation not to occur.
This is a joint work with Rémy Sanchis and Daniel Ungaretti.
More complete information about the seminars can be found at DME
Organizers: Giulio Iacobelli e Maria Eulalia Vares
