Article
Quantum Science & Technology
Tristan Benoist, Lisa Haenggli, Cambyse Rouze
Summary: In this paper, we provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. By introducing and developing new non-commutative functional inequalities, we derive concentration inequalities for stochastic processes that satisfy these bounds. Additionally, we obtain an optimal finite time deviation bound expressed in terms of the non-commutative Dirichlet form.
Article
Mathematics, Applied
Haonan Zhang
Summary: This paper studies the heat smoothing problem for holomorphic subalgebras of free group von Neumann algebras and proves analogous sharp inequalities. In the case of free group von Neumann algebras, the weaker formulation of heat smoothing is proved with optimal order.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics
Rupert L. Frank, Paata Ivanisvili
Summary: This study demonstrates that the Poisson semigroup e(-t root-Delta) on the n-sphere is hypercontractive from L-p to L-q in dimensions n <= 3 when 1 < p <= q, if and only if e(-t root n) <= root p-1/q-1. However, this equivalence fails in large dimensions.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Physics, Multidisciplinary
Niv Levhari, Alex Samorodnitsky
Summary: This article introduces the study of noise operators on the Boolean cube, proving tight results related to the Renyi entropy and norms.
Article
Mathematics
Michael Brannan, Roland Vergnioux, Sang-Gyun Youn
Summary: The study proves that the twisted property RD introduced for non-Kac type, non-amenable orthogonal free quantum groups does not hold, but in the Kac case, there is a analogous result regarding the non-commutative Khintchine inequality for free groups. Additionally, new and improved hypercontractivity and ultracontractivity estimates are provided for the generalized heat semigroups on free orthogonal quantum groups in both Kac and non-Kac cases.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics
Paata Ivanisvili, Alexander Lindenberger, Paul F. X. Muller, Michael Schmuckenschlager
Summary: This paper extends complex uniform convexity estimates to real space R-n and determines the best constants. Furthermore, it establishes a link between log-Sobolev inequalities and hypercontractivity estimates for ultraspherical measures.
REVISTA MATEMATICA IBEROAMERICANA
(2022)
Article
Multidisciplinary Sciences
Satoshi Hayakawa, Harald Oberhauser, Terry Lyons
Summary: Given a probability measure mu on a set chi and a vector-valued function phi, the task is to construct a discrete probability measure on chi that yields the same push-forward as mu under phi. This construction is crucial for numerical integration methods like quadrature, cubature, and recombination. One approach is to sample points from mu until their convex hull under phi includes the mean of phi. By utilizing hypercontractivity and analyzing the computational complexity, this approach covers various cases including multivariate polynomials, integration on pathspace, and kernel quadrature for product measures.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Mathematics
Zoltan M. Balogh, Alexandru Kristaly, Francesca Tripaldi
Summary: The article investigates the sharp L-p-log-Sobolev inequality on noncompact metric measure spaces satisfying the CD(0, N) condition, and proves it using isoperimetric inequality, symmetrization, and scaling argument. It also establishes hypercontractivity estimate for the Hopf-Lax semigroup and obtains Gaussian-type L-2-log-Sobolev inequality and hypercontractivity estimate in RCD(0, N) spaces.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Neal Bez, Shohei Nakamura, Hiroshi Tsuji
Summary: In this paper, deficit estimates for Nelson's hypercontractivity inequality, the logarithmic Sobolev inequality, and Talagrand's transportation cost inequality are provided. The results complement and improve previous studies on inputs with small covariance and for a large class of semi-log-concave inputs. The deficit estimates for each inequality are obtained using different methods, including a flow monotonicity scheme and an optimal transportation argument.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics
Yanqi Qiu, Zipeng Wang
Summary: The paper proposes a definition of branching-type stationary stochastic processes on rooted trees, introduces related definitions of hyper-positivity for functions on the unit circle and non-negative integers, and obtains necessary and sufficient conditions for the existence of non-trivial branching-type stationary stochastic processes on rooted trees. Additionally, the study provides a complete criterion for hyper-positive functions in the setting of rooted homogeneous trees and a prediction theory result for branching-type stationary stochastic processes. Finally, unexpected natural hypercontractive inequalities for Hankel operators with hyper-positive symbols are derived as an application.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics
C. Roberto, B. Zegarlinski
Summary: In this paper, we systematically investigate the hypercontractivity property in Orlicz spaces for Markov semi-groups related to homogeneous and non-homogeneous diffusions in R-n. We provide an explicit construction and prove that the associated hypercontractivity property is equivalent to a suitable functional inequality.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Esther Bou Dagher
Summary: In this paper, we prove the q-logarithmic Sobolev inequality for probability measures in the setting of Carnot groups, and as an application, we use the Hamilton Jacobi equation to prove the p-Talagrand inequality and hypercontractivity.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2022)
Article
Mathematics, Applied
Kazuo Yamazaki
Summary: Recent significant developments in the study of singular partial differential equations have been influenced by techniques borrowed from quantum field theory in physics. This note discusses the necessity of Wick products, their applications through Feynman diagrams, and the utility of Gaussian hypercontractivity theorem, as well as an open problem that is mathematically challenging and physically meaningful. The author aims to make this note accessible to a wide audience by providing sufficient details and including all relevant results necessary for discussions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Yi. C. Huang
Summary: This note considers a variant of a question raised by Mueller and Weissler in 1982, complementing Beckner's classical result on Stein's conjecture and a recent result by Frank and Ivanisvili. It shows that the Poisson semigroup on the n-sphere is hypercontractive from L-p to L-q under certain conditions.
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
(2022)
Article
Mathematics, Applied
Li Gao, Cambyse Rouze
Summary: This study proves that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In addition, the first general approximate tensorization property of the relative entropy is established.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2022)
Article
Statistics & Probability
Elchanan Mussel, Joe Neeman
ANNALS OF PROBABILITY
(2015)
Article
Mathematics, Applied
Elchanan Mossel, Joe Neeman
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2015)
Article
Ecology
Junhyong Kim, Elchanan Mossel, Miklos Z. Racz, Nathan Ross
THEORETICAL POPULATION BIOLOGY
(2015)
Article
Mathematics
Elchanan Mossel, Miklos Z. Racz
Article
Statistics & Probability
Jian Ding, Elchanan Mossel
ELECTRONIC COMMUNICATIONS IN PROBABILITY
(2014)
Article
Computer Science, Information Systems
Siu On Chan, Elchanan Mossel, Joe Neeman
IEEE TRANSACTIONS ON INFORMATION THEORY
(2014)
Letter
Biology
Elchanan Mossel, Mike Steel
JOURNAL OF THEORETICAL BIOLOGY
(2014)
Article
Statistics & Probability
Elchanan Mossel, Allan Sly, Omer Tamuz
PROBABILITY THEORY AND RELATED FIELDS
(2014)
Article
Statistics & Probability
Elchanan Mossel, Joe Neeman, Allan Sly
PROBABILITY THEORY AND RELATED FIELDS
(2015)
Article
Physics, Multidisciplinary
Elchanan Mossel, Mesrob I. Ohannessian
Article
Statistics & Probability
Yuval Filmus, Elchanan Mossel
PROBABILITY THEORY AND RELATED FIELDS
(2019)
Article
Management
Dean Eckles, Hossein Esfandiari, Elchanan Mossel, M. Amin Rahimian
Summary: In this study, the task of selecting k nodes in a social network to maximize the expected spread size of a diffusion is examined. The authors propose algorithms and guarantees to approximate the optimal seed set while limiting the amount of collected network information. They investigate the achievable guarantees using a sublinear influence sample size and develop a probing algorithm to find the seed set with the same approximation guarantee.
OPERATIONS RESEARCH
(2022)
Article
Computer Science, Information Systems
Anuran Makur, Elchanan Mossel, Yury Polyanskiy
Summary: This paper studies the problem of broadcasting on two-dimensional regular grids, which is a specialization of the general broadcasting problem on directed acyclic graphs. The authors make progress towards establishing the conjecture that it is impossible to propagate information in a 2D regular grid regardless of the noise level and the choice of processing function. They prove that recovery of the source vertex X is impossible for any noise level between 0 and 1/2 when all vertices with indegree 2 use either AND or XOR for their processing functions.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Automation & Control Systems
Ali Jadbabaie, Anuran Makur, Elchanan Mossel, Rabih Salhab
Summary: This article presents a new opinion dynamics model in which a group of agents hold inherent and declared opinions. The agents' inherent opinions are fixed and cannot be observed by others. At each time step, agents share their declared opinions on a social network based on their inherent opinions and social pressure. The paper investigates the possibility of estimating agents' inherent opinions from their declared opinions, using the example of predicting election results based on voters' tweets. The analysis shows that estimation of aggregate and individual inherent opinions is possible unless there are large majorities, which cause minorities to lie over time, making asymptotic estimation impossible.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Engineering, Multidisciplinary
Sebastien Bubeck, Elchanan Mossel, Miklos Z. Racz
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2015)