|A short introduction to critical interfaces in 2D (1)|
|michel DOT bauer AT cea DOT fr|
|IPhT CEA Saclay|
|le Monday 21 March 2011 à 09h00|
|Salle de séminaire du groupe de Physique Statistique|
|The purpose of these lectures is very modest. They are meant to introduce
gently to the concepts of Loewner chains, local growth and stochastic
Loewner evolutions (SLEs). These concepts have played an important
role in physics and mathematics during the recent years.
The 1st chapter describes two discrete examples, the exploration process and loop-erased random walks. It can be read almost without any prerequisites. The aim is to show that even for curves dened purely in geometrical terms, it is useful to have a statistical mechanics viewpoint where the measure on curves is derived from a measure on local degrees of freedom of some model. A third model, DLA is also introduced.
The second chapter introduces Loewner chains and their relevance for the description of growth processes. A prerequisite is a minimal knowledge of complex analysis.
The third chapter contains the derivation of the relevance of SLE in the description of interfaces when two properties, conformal invariance and the domain Markov property, are assumed/proved.