## Galen Reeves : Non-asymptotic bounds for approximate message passing via Gaussian coupling

- Probability ( 0 Views )Approximate message passing (AMP) has emerged as a powerful framework for the design and analysis of iterative algorithms for high dimensional inference problems involving regression and low-rank matrix factorization. The basic form of an AMP algorithm consists of a recursion defined on a random matrix. Under suitable conditions, the distribution of this recursion can be well approximated by a Gaussian process whose mean and covariance are defined via a recursive process called state evolution. This talk will briefly summarize some of the key ideas in AMP (no background is assumed). I will then describe a new approach for analyzing these algorithms that constructs an explicit coupling between the AMP iterates and a Gaussian process, Under mild regularity conditions, this coupling argument provides simple and interpretable guarantees on the non-asymptotic behavior of AMP algorithms. Related work can be found in the arXiv papers: https://arxiv.org/abs/2405.08225 and https://arxiv.org/abs/2306.15580

## Vadim Gorin : Six-vertex model in the rare corners regime

- Probability ( 0 Views )The six-vertex model, also known as the square-ice model, is one of the central and most studied systems of 2d statistical mechanics. It offers various combinatorial interpretations. One of them involves molecules of water on the square grid; another one deals with non-intersecting lattice paths, which can be also viewed as level lines of an integer-valued height function. Despite many efforts since the 1960s, the limit shapes for the height function are still unknown in general situations. However, we recently found ways to compute them in a degeneration, which leads to a low density of corners of paths (or, equivalently, of horizontal/vertical molecules of water). I will report on the progress in this direction emphasizing various unusual features: appearance of hyperbolic PDEs; discontinuities in densities; connections to random permutations.

## Ran Tao : Fluctuations of half-space KPZ: from 1/2 to 1/3

- Probability ( 0 Views )We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. We then establish optimal fluctuation exponents for the height function in both the subcritical and critical regimes, along with corresponding estimates for the polymer endpoint. Based on a joint work with Yu Gu.