Article
Mathematics, Applied
Gerard Ben Arous, Aukosh Jagannath
Summary: The objective of this study is to gain a better understanding of the relationship between replica symmetry breaking, shattering, and metastability. To achieve this, we investigated the static and dynamic behavior of spherical pure p-spin glasses above the replica symmetry breaking temperature Ts. Within this range, we identified at least two distinct temperatures associated with non-trivial behavior. Firstly, we demonstrated the existence of a shattering phase in the spherical p-spin model within a temperature regime above but close to Ts. Additionally, we found that metastable states persist up to a higher temperature TBBM, as predicted by Barrat-Burioni-Mezard, which is expected to be higher than the phase boundary for the shattering phase Td.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Mark Sellke
Summary: This study demonstrates that with exponentially close to 1 probability, all near-maximizers of any mean-field mixed p-spin glass Hamiltonian on the hypercube[-1, 1](N) are close to a corner. The proof is elementary and can be extended to arbitrary polytopes with approximately about N^2 faces.
COMPTES RENDUS MATHEMATIQUE
(2021)
Article
Biology
E. A. K. Cohen, A. J. Gibberd
Summary: Wavelets provide flexibility for analyzing stochastic processes at different scales. In this article, we apply wavelets to multivariate point processes to detect and analyze unknown nonstationarity. We develop a temporally smoothed wavelet periodogram to ensure statistical tractability and demonstrate its equivalence to a multi-wavelet periodogram. Under the assumption of stationarity, the distribution of the temporally smoothed wavelet periodogram is shown to be asymptotically Wishart, with readily computable parameters. The distributional results also extend to wavelet coherence, a measure of inter-process correlation. We apply this statistical framework to construct a test for stationarity in multivariate point processes and successfully detect and characterize time-varying dependency patterns in neural spike-train data.
Article
Computer Science, Artificial Intelligence
Claire Launay, Agnes Desolneux, Bruno Galerne
Summary: Determinantal point processes (DPPs) are probabilistic models that favor diversity or repulsion, gaining influence in the machine learning community for their elegant and efficient subsampling capabilities. This paper explores DPPs from an image processing perspective, adapting them for use in sampling pixels or patches of images, known as determinantal pixel processes (DPixPs), to study repulsion properties and apply them to texture synthesis using shot noise models. Additionally, DPPs are also studied for subsampling discrete distributions such as image patches due to their repulsive property.
SIAM JOURNAL ON IMAGING SCIENCES
(2021)
Article
Physics, Multidisciplinary
Maciej Lewenstein, David Cirauqui, Miguel Angel Garcia-March, Guillem Guigo Corominas, Przemyslaw Grzybowski, Jose R. M. Saavedra, Martin Wilkens, Jan Wehr
Summary: The study revisited the approach to the Edwards-Anderson model by evaluating and analyzing the probability distribution of configurations of two replicas of the system, generating squares of thermal copies of spin variables from the two copies of the systems.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Statistics & Probability
Zhou Fan, Song Mei, Andrea Montanari
Summary: This study investigates the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. By considering statistical physics, it is proven that the distance between local minima of the TAP free energy and the mean of the Gibbs measure vanishes in the large size limit. The proof technique involves upper bounding the expected number of critical points of the TAP free energy using the Kac-Rice formula.
ANNALS OF PROBABILITY
(2021)
Article
Geosciences, Multidisciplinary
Tingjin Chu, Yongtao Guan, Rasmus Waagepetersen, Ganggang Xu
Summary: We propose a new estimation method for fitting a semiparametric intensity function model to multivariate spatial point processes. The approach is based on quasi-likelihood and takes into account both between-process and within-process correlations to produce more efficient estimators. The efficacy of the proposed approach is demonstrated through simulations and a real application.
SPATIAL STATISTICS
(2022)
Article
Energy & Fuels
Sergey N. Trukhan, Evgeny V. Morozov, Oleg N. Martyanov
Summary: The work demonstrates the great potential of using a vanadyl porphyrin probe to study resin-paraffin aggregation processes in oils. The dynamics and polarity of the local environment of vanadyl octaethylporphine (VOOEP), used as a spin probe, specially introduced into oil with a high content of paraffins and resins, have been studied. It has been found that VOOEP does not enter into paraffin crystallites but forms aggregates composed of resin molecules that can be adsorbed onto the surface of paraffins.
Article
Biology
Yuchen Yang, Mei-Cheng Wang
Summary: This paper introduces two sets of measures, ASRF/SARF and ARF/SRF, as exploratory tools to study physical activity patterns. A two-level semiparametric regression model is developed for ARF and activity magnitude using marked point process formulation. These measures provide useful analytical tools for practitioners and researchers studying wearable device data.
Article
Computer Science, Information Systems
Nour Kouzayha, Hesham Elsawy, Hayssam Dahrouj, Tareq Y. Al-Naffouri
Summary: This letter explores the meta distribution of the signal to interference ratio (SIR), extending stochastic geometry analysis to provide detailed information about network performance. The development of the meta distribution for the binomial point process allows for analysis of finite point processes, with validation through Monte-Carlo simulations. The newly derived meta distribution for finite point processes shows convergence to the ergodic PPP's meta distribution.
IEEE WIRELESS COMMUNICATIONS LETTERS
(2021)
Article
Statistics & Probability
Matyas Barczy, Bojan Basrak, Peter Kevei, Gyula Pap, Hrvoje Planinic
Summary: This paper focuses on the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton-Watson processes with regularly varying immigration. The limit law is the ratio of two dependent stable random variables with specific indices, and it has a continuously differentiable density function. Point process technique is used in the proofs.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Mathematics, Applied
Maryam Gharamah Ali Alshehri, Eugene Lytvynov
Summary: The paper discusses hafnian point processes on locally compact Polish spaces and their relationship with Cox processes involving Gaussian fields, as well as their application in quantum mechanics.
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
(2022)
Article
Physics, Multidisciplinary
Kirill Amelin, Johan Viirok, Urmas Nagel, Toomas Room, Johannes Engelmayer, Tusharkanti Dey, Agustinus Agung Nugroho, Thomas Lorenz, Zhe Wang
Summary: In this study, high-resolution terahertz spectroscopic techniques were used to investigate the quantum spin dynamics in the quasi-one-dimensional Ising-like ferromagnet CoNb2O6 and antiferromagnet BaCo2V2O8. Confined spinon excitations, E-8 dynamical spectrum, and field-induced quantum phase transitions were observed in the ordered phases stabilized by inter-chain couplings, with the field-dependent evolution of the excitation spectra revealing connections between these characteristic dynamical features.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Automation & Control Systems
Xiangxiang Huang, Xianping Guo, Xin Wen
Summary: This study discusses a two-person zero-sum game for finite-horizon semi-Markov processes, focusing on the probability that the total payoff exceeds a prescribed goal within a finite horizon. The study establishes the Shapley equation and proves the existence of a saddle point under certain conditions. Additionally, a value iterative algorithm is developed to compute an e-saddle point and approximate the game value through solving a series of matrix games. The construction of the e-saddle point and the convergence of the algorithm are also demonstrated. Furthermore, the application of the main results is illustrated using an example on an inventory system.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Multidisciplinary Sciences
Ryan T. White
Summary: This article investigates vector-valued renewal-reward processes on R-d. The jumps of the process are assumed to be independent and identically distributed nonnegative random vectors with mutually dependent components, which can be discrete or continuous. The study utilizes operational calculus techniques and symmetries with respect to permutations to derive a general result for the probability of an arbitrary weak ordering of threshold crossings. The result is analytically and numerically tractable, and its applicability is demonstrated through its application to stochastic network reliability and other special cases.
Article
Mathematics, Applied
Michael Aizenman, Simone Warzel
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2016)
Article
Physics, Mathematical
Michael Aizenman, Manuel Lainz Valcazar, Simone Warzel
JOURNAL OF STATISTICAL PHYSICS
(2017)
Article
Physics, Multidisciplinary
Michael Aizenman, Mira Shamis, Simone Warzel
ANNALES HENRI POINCARE
(2015)
Article
Physics, Mathematical
Michael Aizenman, Hugo Duminil-Copin, Vladas Sidoravicius
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2015)
Article
Mathematics, Applied
Michael Aizenman, Simone Warzel
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2013)
Article
Statistics & Probability
Michael Aizenman, Simone Warzel
PROBABILITY THEORY AND RELATED FIELDS
(2015)
Article
Physics, Mathematical
Michael Aizenman, Simone Warzel
JOURNAL OF STATISTICAL PHYSICS
(2018)
Article
Mathematics
Michael Aizenman, Hugo Duminil-Copin, Vincent Tassion, Simone Warzel
INVENTIONES MATHEMATICAE
(2019)
Article
Physics, Mathematical
Michael Aizenman, Ron Peled
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2019)
Article
Physics, Mathematical
Michael Aizenman, Matan Harel, Ron Peled
JOURNAL OF STATISTICAL PHYSICS
(2020)
Article
Physics, Multidisciplinary
Michael Aizenman, Hugo Duminil-Copin, Simone Warzel
ANNALES HENRI POINCARE
(2020)
Editorial Material
Physics, Mathematical
Michael Aizenman, Ivan Corwin, Juerg Froehlich, Giovanni Gallavotti, Shelly Goldstein, Herbert Spohn
JOURNAL OF STATISTICAL PHYSICS
(2020)
Article
Mathematics
Michael Aizenman, Hugo Duminil-Copin
Summary: This study demonstrates the Gaussian distribution of spin fluctuations in four-dimensional Ising-type models and lambda phi(4) fields with lattice ultraviolet cutoff under certain conditions. The key lies in utilizing the random current representation of the models and improving the tree diagram bound through multi-scale analysis with a logarithmic correction term.
ANNALS OF MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
M. Aizenman, H. Schanz, U. Smilansky, S. Warzel
ACTA PHYSICA POLONICA A
(2017)
Article
Mathematics, Applied
Michael Aizenman, Ron Peled, Jeffrey Schenker, Mira Shamis, Sasha Sodin
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2017)