Article
Physics, Multidisciplinary
O. V. Alekseev
Summary: This study considers a loop representation of the O(n) model at the critical point. In the case of n = 0, the model reduces to statistical ensembles of self-avoiding loops described by Schramm-Loewner evolution (SLE) with kappa = 8/3. The O(n = 0) model corresponds to a logarithmic conformal field theory (LCFT) with the central charge c = 0. The study focuses on LCFT correlation functions in the upper half-plane with twist operators in the bulk and boundary operators Phi(1,2).
THEORETICAL AND MATHEMATICAL PHYSICS
(2023)
Article
Statistics & Probability
Vincent Beffara, Eveliina Peltola, Hao Wu
Summary: This article focuses on the characterization of global multiple Schramm-Loewner evolutions (SLE) and proves the existence of a unique probability measure for describing collections of pairwise disjoint continuous simple curves, leading to the convergence of multiple interfaces in critical lattice models.
ANNALS OF PROBABILITY
(2021)
Article
Mathematics
Yilin Wang
Summary: The expression of Loewner energy for a Jordan curve was established using Werner's measure on simple loops of SLE8/3 type. The proof is based on a formula for the change of Loewner energy under a conformal map reminiscent of the conformal restriction property of SLE processes.
ANNALES DE L INSTITUT FOURIER
(2021)
Article
Physics, Multidisciplinary
Makoto Katori, Shinji Koshida
Summary: This paper discusses properties of multiple Schramm-Loewner evolutions (SLEs) labelled by a parameter kappa is an element of (0, 8], and proves the conjecture that the solution indeed generates multiple continuous curves.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Mathematics
Oliver McEnteggart, Jason Miller, Wei Qian
Summary: The article introduces a set of geometric conditions on curves for the mapping φ to be a conformal automorphism of H, which can be applied to random conformal welding problems related to SLE and LQG. Specifically, it establishes that φ is a conformal automorphism of H under certain conditions, providing new insights for critical LQG and the welding of stable looptrees.
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU
(2021)
Article
Statistics & Probability
Pu Yu
Summary: Chordal SLE,(rho) is a variant of the chordal SLE curve that is influenced by additional force points. The law of SLE,(rho) is not reversible when there are force points away from the origin. Zhan (2019) provides a description of the time reversal of SLE,(rho) and conjectures its general applicability. In this paper, we prove his conjecture.
ELECTRONIC JOURNAL OF PROBABILITY
(2023)
Article
Statistics & Probability
Vivian Olsiewski Healey, Gregory F. Lawler
Summary: The paper presents the definition of n-radial SLE by interpreting the Schramm-Loewner evolution as a limit of path measures tilted by a loop term. It justifies the definition by proving the existence of a limit measure obtained from appropriately normalized loop terms on n-tuples of paths. The limit measure describes n paths moving by the Loewner equation with a driving term of Dyson Brownian motion.
PROBABILITY THEORY AND RELATED FIELDS
(2021)
Article
Statistics & Probability
Frankie Higgs
Summary: In this study, we analyzed a planar random aggregation model and discovered a phase transition in the attachment distribution. The model exhibits atomic attachment distribution in certain conditions, and the cluster converges to a Schramm-Loewner evolution with parameter kappa = 4. We also conjectured that similar results can be obtained using other particle shapes from a certain family.
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
(2022)
Review
Physics, Multidisciplinary
Shai M. Chester
Summary: These lectures aim to familiarize students with the nuts and bolts of numerical bootstrap in an efficient manner, covering the basics of conformal field theory, computation of conformal blocks, formulation of crossing equations as a semi-definite programming problem, solving the problem using SDPB, and interpretation of the results. The lectures include worked examples and problem sets to help students master the skills, culminating in a precise computation of the critical exponents of the 3d Ising model.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2023)
Article
Statistics & Probability
Juhan Aru, Titus Lupu, Avelio Sepulveda
Summary: This article investigates the properties of CLE4 in the unit disk and determines the law of the conformal radius seen from the origin and the extremal distance to the boundary of the disk. Surprisingly, it also computes the joint law of these two quantities. The study involves the first and last hitting times of a one-dimensional Brownian motion, and similar techniques are applied to determine joint laws of extremal distances in a critical Brownian loop-soup cluster.
ANNALS OF PROBABILITY
(2022)
Article
Statistics & Probability
Eveliina Peltola, Hao Wu
Summary: We prove that the crossing probabilities of multiple interfaces in the critical planar Ising model with alternating boundary conditions are conformally invariant expressions given by the pure partition functions of multiple SLE & kappa; with & kappa; = 3 in the scaling limit. This identifies the scaling limits with ratios of specific correlation functions of conformal field theory.
ANNALS OF APPLIED PROBABILITY
(2023)
Article
Statistics & Probability
Jason Miller, Scott Sheffield, Wendelin Werner
Summary: This study explores the relationship between simple conformal loop ensembles (CLE kappa) and independent root kappa-Liouville quantum gravity (LQG) surfaces, revealing that the cut out quantum surfaces form a Poisson point process of quantum disks. This construction allows for direct connections between CLE on LQG, stable processes, and branching trees, leading to various consequences such as constructing CLE on LQG as a patchwork of quantum disks and deriving new properties and formulas for SLE processes.
ANNALS OF PROBABILITY
(2022)
Article
Statistics & Probability
Jason Miller, Scott Sheffield
Summary: We endowed the 8/3-root Liouville quantum gravity sphere with a metric space structure and demonstrated that the resulting metric measure space is in law agreement with the Brownian map. By extending the metric from a countable dense subset to the entire Euclidean sphere S-2, we established properties such as Holder continuity in both directions for the identity map between different metric spaces. Additionally, we provided analogous results for the Brownian disk and plane, exploring new estimates on the size and shape of quantum surfaces along the way.
ANNALS OF PROBABILITY
(2021)
Article
Statistics & Probability
Mingchang Liu, Hao Wu
Summary: The crossing probabilities of the metric graph Gaussian free field (GFF) defined on polygons of delta Z(2) with alternating boundary data have scaling limits. When the boundary data is well-chosen, the scaling limits of crossing probabilities can be explicitly constructed as fusion of multiple SLE4 pure partition functions.
ELECTRONIC JOURNAL OF PROBABILITY
(2021)
Article
Astronomy & Astrophysics
Stefano Baiguera, Sara Bonansea, Kristian Toccacelo
Summary: By computing holographic complexity for the nonsupersymmetric Janus deformation of AdS5, we found the appearance of a subleading logarithmic divergent term and a finite part in the volume complexity of the corresponding subregion located around the interface. We also discovered that the coefficient of the logarithmic term is universal for two different regularization prescriptions of the divergences.
Article
Mechanics
Hugo Ricateau, Leticia F. Cugliandolo, Marco Picco
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2018)
Article
Mechanics
Leticia F. Cugliandolo, Gustavo S. Lozano, Nicolas Nessi, Marco Picco, Alessandro Tartaglia
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2018)
Review
Physics, Mathematical
Nikolaos G. Fytas, Victor Martin-Mayor, Marco Picco, Nicolas Sourlas
JOURNAL OF STATISTICAL PHYSICS
(2018)
Article
Mechanics
Alessandro Tartaglia, Leticia F. Cugliandolo, Marco Picco
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2018)
Article
Mechanics
Federico Corberi, Leticia F. Cugliandolo, Ferdinando Insalata, Marco Picco
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2019)
Article
Physics, Multidisciplinary
Nikolaos G. Fytas, Victor Martin-Mayor, Giorgio Parisi, Marco Picco, Nicolas Sourlas
PHYSICAL REVIEW LETTERS
(2019)
Article
Mechanics
N. G. Fytas, Victor Martin-Mayor, Giorgio Parisi, Marco Picco, Nicolas Sourlas
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2019)
Article
Physics, Multidisciplinary
Damien Barbier, Leticia F. Cugliandolo, Gustavo S. Lozano, Nicolas Nessi, Marco Picco, Alessandro Tartaglia
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2019)
Article
Physics, Fluids & Plasmas
Nikolaos G. Fytas, Victor Martin-Mayor, Giorgio Parisi, Marco Picco, Nicolas Sourlas
Summary: This article investigates the problem of finite-size scaling above the upper critical dimension for disordered systems. The results confirm the successful application of a modified version of finite-size scaling in the context of the random-field problem.
Article
Physics, Multidisciplinary
Marco Picco, Sylvain Ribault, Raoul Santachiara
Proceedings Paper
Physics, Multidisciplinary
F. Corberi, L. F. Cugliandolo, M. Esposito, M. Picco
9TH YOUNG RESEARCHER MEETING
(2019)
Proceedings Paper
Physics, Applied
F. Insalata, F. Corberi, L. F. Cugliandolo, M. Picco
8TH YOUNG RESEARCHER MEETING, 2017
(2018)
Article
Physics, Fluids & Plasmas
A. Crisanti, M. Picco, F. Ritort
Article
Physics, Fluids & Plasmas
Federico Corberi, Leticia F. Cugliandolo, Ferdinando Insalata, Marco Picco
Article
Physics, Fluids & Plasmas
Nikolaos G. Fytas, Victor Martin-Mayor, Marco Picco, Nicolas Sourlas