- Docente: Pierluigi Contucci
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
At the end of the course the student is familiar with the advanced notions on statistical mechanics topics and its socio-economic applications. He is able to investigate independently the novel topics of the discipline from research papers.
Course contents
- Introductive
lecture
- Probability
Spaces
-
Entropy
- Simplexes and probability
spaces.
- Particle systems and Ising
models.
- Ising model in d=1 with free
and periodic boundary conditions.
- Dichotomic functions and
their Fourier expansion.
- Simple notions for Ising
models at d>1
- The thermodynamic limit and
correlation inequalities.
- Mean field models.
Curie-Weiss model.
- Thermodynamic limit for mean
field models.
- The solution of the Curie
Weiss model with boundary from above and
below.
- Large number theorem and
central limit theorem for the magnetization. Free model and model
with interaction.
- Large deviation theory and
solution of the Curie Weiss model.
- Theoretical inverse problem:
from thermodynamic quantities to
parameters.
- Phenomenological inverse
problem: from real data to thermodynamic
quantities.
- Maximum likelihood
method.
Readings/Bibliography
"Perspectives on Spin Glasses", Pierluigi Contucci e Cristian Giardina, Cambridge University Press
Teaching methods
Class lectures, examples, and exercises. Computer simulations illustrations. In case international students will be attending the course the lectures will be in english.
Assessment methods
The exam test is of oral type and possibly, if the student is interested, can take the form of a simple research seminar. The final grade will be computed as the average of two modules. The exam has the purpose to prove that the student has assimilated the fundamentals concepts and is able to develop rigorous proofs on the course content.
Teaching tools
Some lectures, especially those on the inverse problem, will be given by showing computer simulations or data elaboration.
Links to further information
http://www.dm.unibo.it/~contucci/lectiones.html
Office hours
See the website of Pierluigi Contucci