Summer School in Mathematical Physics

Rigorous Results in Statistical Mechanics
and
Quantum Field Theory

Talks

Haji Ahmedov (FGE)


Cavity Shape and Casimir Energy

Abstract:

Levent Akant (FGE)


Equivariant Symplectic Geometry of Gauge Fixing in Yang-Mills Theory

Abstract:

Nihat Berker (Koç Uni)


Phase Diagrams of the d=3 Electronic Conduction Models with Frozen Impurities: Renormalization-Group Calculations

Abstract:

Michael Hinczewski (FGE)


The Tensor Renormalization-Group: Novel Approaches to Calculating High Precision Thermodynamic Properties of Classical Lattice Hamiltonians

Abstract:

Muhittin Mungan (FGE & Boğaziçi Uni)


String Matching and 1d Lattice Gases

Abstract: In this talk I will consider the probability distribution for the number of occurrences of a given word inside a random string whose letters have been generated by a stationary stochastic process. The problem is non-trivial due to the possibility of overlapping occurences and has applications in communication theory and analysis of biological sequences. I will show that this problem can be cast into one of determining the partition function of a 1d lattice gas with interacting particles. Using this analogy, the probability distribution can be obtained from a virial expansion. It turns out that the properties of the stochastic process as well as the specifics of the word to be searched only serve to furnish the effective interactions between the particles of the lattice gas, which turn out be rather generic: they are pairwise, of nearest neighbour type and characterized by a relatively strong core of size of the word length that is followed by a weak and exponentially decaying tail.

Slides

Teoman Turgut (FGE & Boğaziçi Uni)


Lee Model

Slides