Innovating Works

UniversalMap

Financiado
Universality of random planar maps and trees
The PI proposes to study a variety of open problems involving random planar maps and trees. This is a booming field at the intersection of probability, geometry, statistical physics, combinatorics and complex analysis. It has grow... The PI proposes to study a variety of open problems involving random planar maps and trees. This is a booming field at the intersection of probability, geometry, statistical physics, combinatorics and complex analysis. It has grown tremendously in the last two decades, in depth and breadth, and has seen breakthroughs on long-standing classical problems. The PI's first goal is to study the universality of embedded random planar maps and prove their convergence to what is known as Liouville quantum gravity, a class of random surfaces predicted by physicists to be the universal limit to such discrete random surfaces. Various map embedding mechanisms will be studied such as harmonic embedding, square-tiling, circle packing and others. The second goal is to solve problems concerning stochastic processes (such as random walks, percolation and the Ising model) on embedded random planar maps. This will shed light on the behavior of the same stochastic processes on regular lattices (such as the square or triangular grids) due to the non-rigorous Knizhnik-Polyakov-Zamolodchikov correspondence, a conjectural formula from the physics literature relating the behavior of critical statistical physics models on random lattices to their behavior on regular lattices. We will gain progress on these inspiring yet non-rigorous predictions by developing various probabilistic, geometric and complex analytic tools aimed to show that instabilities in the embeddings cancel out due to the randomness of the planar maps. This project has the potential to lead to the solution of the most central problems in two-dimensional statistical physics, such as estimating the typical displacement of the self-avoiding walk, proving conformal invariance for critical percolation on the square lattice and many others. ver más
31/12/2026
TAU
2M€
Perfil tecnológico estimado
Duración del proyecto: 72 meses Fecha Inicio: 2020-12-18
Fecha Fin: 2026-12-31

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2020-12-18
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2020-COG: ERC CONSOLIDATOR GRANTS
Cerrada hace 4 años
Presupuesto El presupuesto total del proyecto asciende a 2M€
Líder del proyecto
TEL AVIV UNIVERSITY No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5