Statistical mechanics models undergoing a phase transition often exhibit rich, fractal-like behaviour at their critical points, which are described in part by critical exponents, the indices governing the power-law growth or decay of various...

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Probability Seminar

The Loewner energy is a Möbius invariant quantity that measures the roundness of Jordan curves on the Riemann sphere. It arises from large deviation deviations of SLE0+ and is also a Kähler potential on the Weil-Petersson Teichmüller space...

### Large deviations for random hives and the spectrum of the sum of two random matrices

Hives, as defined by Knutson and Tao, are discrete concave functions on a triangular grid on an equilateral triangle of side n. It is known through the work of Knutson and Tao that the probability distribution of the spectrum of the sum of two...

We consider the Schramm-Loewner evolution (SLE_{kappa}) for kappa in (4,8), which is the regime that the curve is self-intersecting but not space-filling. We let K be the set of kappa in (4,8) for which the adjacency graph of connected components of...

Planar last passage percolation models are canonical examples of stochastic growth, polymers and random geometry in the Kardar-Parisi-Zhang universality class, where one considers oriented paths between points in a random environment accruing the...

In the first story we wonder about the ubiquity of the free field and look at a few characterisation theorems. In the second story we discuss the mutually benefiting relationship between the discrete free field and the O(N) spin model. Finally, in...

Through the random matrix analogy, Fyodorov, Hiary and Keating conjectured very precisely the typical values of the Riemann zeta function in short intervals of the critical line, in particular their maximum. Their prediction relied on techniques...

In Euclidean geometry, bisectors are perpendicular lines. In random plane geometry, the situation is more complicated. I will describe bisectors in the directed landscape, the universal geometry in the KPZ class. These help answer some open...

Liouville conformal field theory is a CFT with central charge c>25 and continuous spectrum, its correlation functions on Riemann surfaces with marked points can be expressed using the bootstrap method in terms of conformal blocks. We will explain...

Liouville conformal field theory is a CFT with central charge c>25 and continuous spectrum, its correlation functions on Riemann surfaces with marked points can be expressed using the bootstrap method in terms of conformal blocks. We will explain...