This term, all seminars take place Thursdays at 2pm, room MS.04 (Zeeman Building), unless indicated otherwise.

Schedule for

Nils Berglund, 19.01.2017



04.05.2017 Tobias Kuna (University of Reading)
Density expansion of the truncated and the direct correlation function
Particle systems interacting via translation invariant pair potentials are among the most intractable point processes if one is outside the high temperature low activity regime (HTLAR). In particular, the liquid regime is of paramount interest in chemistry and engineering, but the available theory is phenomenological. Chemists and physicists have derived a rather satisfactory description for the thermodynamics of simple liquids which works far outside the HTLAR exploiting correlation functions and postulation relations between them based on formal expansion in the density, so called moment closures. However, it is also acknowledged that {it ``the manipulations involved in obtaining these infinite sums ... have been carried out in a purely formal way and we have not examined the important but difficult questions of convergence and the legitimacy of the rearrangement of terms”} even in HTLAR. Mathematically the difficulty is to find for a sum $e^{n^2}$ terms (each of them an $n$-dimensional integral) a bound of order $e^{nln(n)}$. The classical technique of cluster expansion of abstract polymer models enables us to achieve this. The cluster expansion in the canonical ensemble is recalled. The correlation and in particular the direct correlation lead to an expansion in terms for graphs of a different combinatorial nature which cannot be treated in the same way as the previous cases considered in the canonical ensemble. The cancelation, which are of combinatorial nature, have to hold exactly to make this estimation possible. This is joint work with Dimitrios Tsagkarogiannis.
Contact: Daniel

18.05.2017 Nikos Fytas (Coventry University)
Phase transitions in disordered systems: The example of the random-field Ising model
In Statistical Physics, more often than not, the behavior of a strongly disordered system cannot be inferred from its clean, homogeneous counterpart. In fact, disordered systems are prototypical examples of complex entities in many aspects, mainly in the rough free-energy landscape profile. In the current talk, I will present some new results relevant to critical phenomena and universality aspects of disordered systems using as a platform the random-field Ising model at several spatial dimensionalities (below the upper critical one).
Contact: Nikos


08.06.2017 Sasha Sodin (Queen Mary University)
Random matrices and random Young diagrams
The rows of a Young diagram chosen at random with respect to the Plancherel measure are known to share some features with the eigenvalues of the Gaussian Unitary Ensemble. We shall discuss several ideas, going back to the work of Kerov and developed by Biane and by Okounkov, which to some extent clarify this similarity, and allow to apply some of the methods of random matrix theory to the study of random Young diagrams. Partially based on joint work with In-Jee Jeong
Contact: Nikos
15.06.2017 Atilla Yilmaz (Koc)
Nonconvex homogenization for one-dimensional controlled random walks in random potential
In this talk, we will consider a finite horizon stochastic optimal control problem for nearest-neighbor random walk ${X_i}$ on the set of integers. The cost function involves the exponential of the path sum of a random potential plus $ heta X_n$. The random walk policies are measurable with respect to the random potential, with their drifts uniformly bounded in magnitude by a parameter $deltain[0,1]$. Under natural conditions on the potential, we prove that the normalized logarithm of the optimal cost function converges. The Bellman equation associated to this control problem is a second-order Hamilton-Jacobi (HJ) stochastic partial difference equation. We prove that this equation homogenizes to a first-order HJ deterministic partial differential equation. The convexity/nonconvexity in $ heta$ of the effective Hamiltonian is characterized by a simple inequality involving $delta$ and the magnitude of the potential, thereby marking two qualitatively distinct control regimes. Based on recent joint work with Ofer Zeitouni.
Contact: Nikos