Schedule Summer School Randomness in Physics & Mathematics(week 1 = 01. - 06. August 2022 & week 2 = 08. - 13. August 2022)
week 1
9:15
9:30-10:30
coffee11-12
lunch 12:30
14-15

MondayTuesday
welcomeBourgade Maı̈da

WednesdayThursdayFridaySaturday

Dumitriu

SchehrDumitriu

Maı̈daDumitriu

BourgadeMaı̈daMaı̈daDumitriu

SchehrSchehrexcursion
Open-Air

15-16:30
coffee17-18

exercises

exercises

talks∗

exercises

Museumsolutionssolutionsposters∗

exercises
female career
solutionssolutionsDetmold +18:15

concertBiergarten

19:15

barbecueDetmold

week 2

MondayTuesday

WednesdayThursdayFridaySaturday9:30-10:30
Katoricoffee11-12
Prosenlunch 12:30
14-15
ClaeysWarzelClaeysWarzelProsenKatori

Katori

WarzelProsenClaeysClaeysProsentalks∗

WarzelKatorideparture

15-16:30
coffee17-18

exercises

exercises

talks∗

exercises

exercises

solutionssolutionsposters∗

solutionssolutions

18:15

barbecue

SchehrBourgade Bourgade talks∗∗

see separate Wednesday afternoon’s programme

Lecture titles week 1:• Paul Bourgade: Branching processes in random matrix theory and number theory• Ioana Dumitriu: Combinatorial methods in random graph theory• Mylène Maı̈da: Determinantal point processes and related topics• Grégory Schehr: Fermionic systems and random matrix theory

concert: ”Last Silence” Markus Schwartze (piano) and Veit Mette (projections)Lecture titles week 2:• Tom Claeys: Riemann-Hilbert techniques for determinantal point processes• Makoto Katori: Point processes and multiple-SLE/GFF coupling• Tomaž Prosen: Many body quantum chaos with dual unitary circuits• Simone Warzel: A guide to rigorous results on quantum spin glasses

Abstracts/Literature/Recommendations for the lectures:• Paul Bourgade: I will first review the principles to characterize extrema for branching processes. I will then focus on implementation of these methods for predictions
by Fyodorov, Hiary and Keating, which link the maximum of random characteristic
polynomials and the maximum of the Riemann zeta function on most short intervals
along the critical line.
• Ioana Dumitriu: Graphs are incredibly useful objects used for modeling in a wide
variety of fields of science and technology, from physics to biology, genomics, chemistry, information theory, and (more recently) machine learning and data science.
Often, the applications require the model to be random, or rely on certain properties that random models satisfy with high probability (thus, that the ”typical”
graph from a certain class of graphs satisfy). We will examine some of the mostwidely known random graph models, their connectivity properties which relate totheir spectrum, and present some of the combinatorial methods (some ”imported”
from random matrix theory, and some developed specifically with graphs in mind)
that allowed us to study and understand their spectra. We will also mention noncombinatorial methods that allow for a closer, more refined study of the spectrum,
as well as applications.
Lecture 1: Graphs, random graphs, and random matrices
Lecture 2: The Erdos-Renyi model and its properties
Lecture 3: Random regular and bipartite biregular graphs
Lecture 4: Generalizations• Schehr: short review:
D. S. Dean, P. Le Doussal, S. N. Majumdar, G. Schehr, Noninteracting fermionsin a trap and random matrix theory, J. Phys. A: Math. Theor. 52 144006 (2019),
https://arxiv.org/abs/1810.12583
more advanced references:
D. S. Dean, P. Le Doussal, S. N. Majumdar, G. Schehr, Finite temperature freefermions and the Kardar-Parisi-Zhang equation at finite time, Phys. Rev. Lett.
114, 110402 (2015), https://arxiv.org/abs/1412.1590
D. S. Dean, P. Le Doussal, S. N. Majumdar, G. Schehr, Non-interacting fermionsat finite temperature in a d-dimensional trap: universal correlations, Phys. Rev. A
94, 063622 (2016), https://arxiv.org/abs/1609.04366

• Tom Claeys:Lecture 1: Introduction to determinantal point processesLecture 2: Transformations of determinantal point processes
Lecture 3: The Its-Izergin-Korepin-Slavnov method and its variants
Lecture 4: Asymptotics and integrable differential equations• Makoto Katori:(i) a variety of determinantal point processes (DPPs), and(ii) the Gaussian analytic functions (GAFs) on a disk and an annulus, and point
processes given by zeros of the GAFs.
(iii) the Brownian motion, the Bessel process, the Schramm-Loewner evolution(SLE), Dyson’s Brownian motion,(iv) the Gaussian free field (GFF) and the coupling between GFF and the multiple
SLE driven by Dyson’s Brownian motion. Notice that Dyson’s Brownian motion
with beta=2 can be regarded as a dynamical version of DPP.
https://link.springer.com/book/10.1007/978-981-10-0275-5
https://www.worldscientific.com/doi/abs/10.1142/S2010326322500253
https://link.springer.com/article/10.1007/s00220-022-04365-2
https://arxiv.org/abs/2011.10291• Tomaž Prosen: Literature
Exact Correlation Functions for Dual-Unitary Lattice Models in 1 + 1 Dimensions
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.210601
Ergodic and Nonergodic Dual-Unitary Quantum Circuits with Arbitrary Local Hilbert
Space Dimension
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.100603
Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
https://link.springer.com/article/10.1007/s00220-021-04139-2
Many-body quantum chaos and dual-unitarity round-a-facehttps://aip.scitation.org/doi/10.1063/5.0056970

Wednesday Afternoon’s Programme
Wednesday 03.08.
14:00 – 14:15
14:20 – 14:35
14:40 – 14:55
15:00 – 15:15
15:15 – 15:30
15:35 – 15:50
15:55 – 16:3016:30 – 17:30

week 1
BhosaleByun
Parrabreak
M. KumarLobaskincoffeeposter 1.-5.

Wednesday 10.08.
14:00 – 14:15
14:20 – 14:35
14:40 – 14:55
15:00 – 15:15
15:15 – 15:30
15:35 – 15:50
16:30 – 17:30

week 2
Crumpton
K. Kumar
Van Werde
break
Borji
Ferizović
coffeeposter 6.-11.

Talk Titles:• Uday Bhosale: Higher-order spacing ratios in random matrices: a review• Majdouline Borji: Pertubative renormalization by flow equations• Sung-Soo Byun: On the characteristic polynomial of the eigenvalue moduli of random normal matrices• Mark Crumpton: Distribution of eigenvalues and singular values in low-rank matrices with non-negative entries• Damir Ferizović: Spherical cap discrepancy of perturbed lattices under the Lambert
projection• Kiran Kumar: On limiting moments of Linear eigenvalue statistics of Hankel matrices• Manoj Kumar: Critical properties in a disordered Potts model• Ivan Lobaskin: Integrable asymmetric exclusion processes with a defect particle• Iván Parra: Planar orthgonal polynomials as type I orthogonal polynomials• Alexander Van Werde: Singular value distribution of dense random matrices withblock Markovian dependence
Poster Titles: (3.8. poster 1.-5.; 10.8. poster 6.-11.)
1. Nedialko Bradnioff: Benford’s Law and the Circular β-ensembles.
2. Anastasis Kafetzopoulos : Local Marchenko-Pastur law
3. Wenkui Liu: Limit Shape and Fluctuation of q-Orthogonal Polynomial Ensembles
4. Azadeh Malekan: Exact finite-size scaling for the random-matrix representation ofbond percolation on square lattice
5. Svetlana Malysheva: Eigenvalue statistics of half-heavy random matrices

6. Leslie Molag: The Elliptic Ginibre Ensemble: A Unifying Approach to Local andGlobal Statistics for Higher Dimensions
7. Goran Nakerst: Sparse Random Markov Generators
8. Okar Prośniak: Non-perturbatively slow dissipation in almost localized chains
9. Haixiao Wang: Particial recovery and weak consistency in non-uniform hypergraphstochastic block model
10. Tim Würfel: Averages of characteristic polynomials for invertible ensembles, multicontour integral formulas and universality
11. Meng Yang: Universality in Random Normal Matrix Models with Merging Singularity