Probability

Subject:

Read more about Interacting Particle Systems 9
4486 reads

Random Maps 9

Speaker:

Gregory Miermont

Date:

Mon, Jun 18, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

The study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

Class:

Subject:

Read more about Random Maps 9
4500 reads

Interacting Particle Systems 8

Speaker:

Omer Angel

Date:

Fri, Jun 15, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

Particles attempt to follow a simple dynamic (random walk, constant flow, etc) in some space (interval, line, cycle, arbitrary graph). Add a simple interaction between particles, and the behaviour can change completely. The resulting dynamical systems are far more complex than the ingredients suggest. These processes (interchange process, TASEP, sorting networks, etc) have diverse to many topics: growth processes, queuing theory, representation theory, algebraic combinatorics. I will discuss recent progress on and open problems arising from several models of interacting particle systems.

Class:

Subject:

Read more about Interacting Particle Systems 8
4446 reads

Limit theorems for conditioned non-generic Galton-Watson trees

Speaker:

Igor Kortchemski

Date:

Thu, Jun 14, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

We are interested in a particular type of subcritical Galton-Watson trees, which are called non-generic trees in the physics community. In contrast with the critical or supercritical case, it is known that condensation appears in large conditioned non-generic trees, meaning that with high probability there exists a unique vertex with macroscopic degree comparable to the total size of the tree. We investigate this phenomenon by studying scaling limits of such trees. In particular, we show that the height of such trees grows logarithmically in their size.

Class:

Subject:

Interacting Particle Systems 7

Speaker:

Omer Angel

Date:

Tue, Jun 19, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

Particles attempt to follow a simple dynamic (random walk, constant flow, etc) in some space (interval, line, cycle, arbitrary graph). Add a simple interaction between particles, and the behaviour can change completely. The resulting dynamical systems are far more complex than the ingredients suggest. These processes (interchange process, TASEP, sorting networks, etc) have diverse to many topics: growth processes, queuing theory, representation theory, algebraic combinatorics. I will discuss recent progress on and open problems arising from several models of interacting particle systems.

Class:

Subject:

Read more about Interacting Particle Systems 7
4322 reads

Random Maps 7

Speaker:

Gregory Miermont

Date:

Thu, Jun 14, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

The study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

Class:

Subject:

Read more about Random Maps 7
4586 reads

Local relaxation for FA-1f out of equilibrium

Speaker:

Oriane Blondel

Date:

Tue, Jun 12, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

We consider the Fredrickson and Andersen one spin facilitated model (FA1f)on Z^d. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability p or q=1-p respectively, provided that at least one of its nearest neighbours is empty. We study the non-equilibrium dynamics started from an initial distribution $\nu$ different from the stationary product p-Bernoulli measure $\mu$, which has enough zeros. We then prove local convergence to equilibrium when the vacancy density q is above a proper threshold. The convergence is exponential (d=1) or stretched exponential (d>1). Joint work with N. Cancrini, F. Martinelli, C. Roberto and C. Toninelli.

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Subject:

Read more about Local relaxation for FA-1f out of equilibrium
5168 reads

Random Maps 6

Speaker:

Gregory Miermont

Date:

Tue, Jun 12, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

The study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

Class:

Subject:

Read more about Random Maps 6
4587 reads

Interacting Particle Systems 6

Speaker:

Omer Angel

Date:

Tue, Jun 12, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

Particles attempt to follow a simple dynamic (random walk, constant flow, etc) in some space (interval, line, cycle, arbitrary graph). Add a simple interaction between particles, and the behaviour can change completely. The resulting dynamical systems are far more complex than the ingredients suggest. These processes (interchange process, TASEP, sorting networks, etc) have diverse to many topics: growth processes, queuing theory, representation theory, algebraic combinatorics. I will discuss recent progress on and open problems arising from several models of interacting particle systems

Class:

Subject:

Read more about Interacting Particle Systems 6
4536 reads

Finite range decomposition of Gaussian fields

Speaker:

Roland Bauerschmidt

Date:

Tue, Jun 12, 2012

Location:

PIMS, University of British Columbia

Conference:

PIMS-MPrime Summer School in Probability

Abstract:

I will show how to decompose the Gaussian free field on a (weighted) graph into a sum of finite range Gaussian fields, which are smoother than the original field and have spatially localized correlations.

Class:

Subject: