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Número de ramificación y percolación de un pseudogrupo
- Autor/a
- Pérez Fernández de Córdoba, María
The branching number of a rooted tree represents the average number of
branches per vertex. This number is strongly related with Bernoulli
percolation process, which involves removing edges at random on the
tree and whose goal is to study the nature of the resulting clusters.
We extend these notions to any measurable pseudogroup of finite type
on a probability space. We prove that if the branching number is equal
to 1 then the pseudogroup is amenable. In fact, when the measure is
harmonic, the pseudogroup is Liouville. Regarding Bernoulli
percolation, we remove edges at random on the orbits and we define a
critical percolation. We study the influence of the number of ends of
the orbits on the critical percolation. Finally, we define the
percolation relative to a Borel set on group actions on a probability
space, keeping the edges whose endpoints belong to the Borel set and
removing the others. We use again the number of ends in order to
achieve information about the clusters.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Editorial
- Universidade de Santiago de Compostela. Servizo de Publicacións e Intercambio Científico
- Publication Year
- 12/04/2013
- File Size
- 1.3 MB
- Serie
- Publicaciones del Departamento de Geometría y Topología
- ISBN
- 9788489390416
- Availability
- Si
The branching number of a rooted tree represents the average number of
branches per vertex. This number is strongly related with Bernoulli
percolation process, which involves removing edges at random on the
tree and whose goal is to study the nature of the resulting clusters.
We extend these notions to any measurable pseudogroup of finite type
on a probability space. We prove that if the branching number is equal
to 1 then the pseudogroup is amenable. In fact, when the measure is
harmonic, the pseudogroup is Liouville. Regarding Bernoulli
percolation, we remove edges at random on the orbits and we define a
critical percolation. We study the influence of the number of ends of
the orbits on the critical percolation. Finally, we define the per...