Article
Physics, Mathematical
Sarai Hernandez-Torres, Eviatar B. Procaccia, Ron Rosenthal
Summary: In this study, we investigate the time constant rho(u) associated with chemical distance in random interlacements at low intensity u << 1 in Z(d) with d >= 5. We prove an upper bound of order u(-1/2) and a lower bound of order u(-1/2+epsilon). The upper bound confirms the conjectured scale in which u(1/2)rho(u) converges to a constant multiple of the Euclidean norm as u -> 0. Additionally, we obtain a local lower bound on the chemical distance between the boundaries of two concentric boxes, which may have independent significance. The paper utilizes probabilistic bounds as u -> 0 for both upper and lower bounds, which can be relevant in future studies of low-intensity geometry.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics
Hector Eduardo Roman, Fabrizio Croccolo
Summary: The article discusses network models as a framework for describing the spread of infectious diseases, using two types of random structures as building blocks. It analyzes the time evolution of susceptible, infected, and recovered individuals during the spread of an infectious disease, and discusses the implementation of lockdowns and simulation methods. The article also presents numerical and analytical results for percolation clusters and random trees, concluding that hierarchical networks can complement the SIR model in most circumstances.
Article
Physics, Multidisciplinary
Paulo Murilo C. de Oliveira, Daniel A. Stariolo, Jeferson J. Arenzon
Summary: The size and shape of the affected region play a crucial role in understanding disease dynamics and organizing future actions. This study explores a modified SIR model where agents diffuse on a lattice, and disease transmission occurs between infected and susceptible agents that are nearest neighbors. The research investigates the geometric properties of the outbreak and unvisited clusters, finding a hybrid transition separating a finite outbreak cluster from one that percolates through the system. Additionally, the outbreak cluster exhibits similar behavior to the critical cluster of ordinary percolation, while clusters with unvisited sites have a size distribution with a Fisher exponent tau < 2.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Mathematics
Jonathan Hermon, Tom Hutchcroft
Summary: This study shows that infinite clusters in supercritical percolation on non-amenable transitive graphs almost surely exhibit anchored expansion. Additionally, various observables on such graphs, including percolation probability, truncated susceptibility, and truncated two-point function, are analytic functions of p throughout the supercritical phase.
INVENTIONES MATHEMATICAE
(2021)
Article
Physics, Mathematical
Alexandra Quitmann, Lorenzo Taggi
Summary: We study a system of interacting random loops, encompassing several interesting models such as the Spin O(N) model, random lattice permutations, a version of the interacting Bose gas in discrete space, and the loop O(N) model. We investigate the system in Z(d), d >= 3, and prove the existence of macroscopic loops whose length is proportional to the volume of the system. Our results hold under general assumptions on the interaction potential, which can have bounded or unbounded support or introduce hard-core constraints.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Statistics & Probability
Subhajit Goswami, Pierre-Francois Rodriguez, Franco Severo
Summary: This paper considers the Gaussian free field phi on Z(d), and provides sharp bounds on the probability of the radius of a finite cluster exceeding a given value for any height. The results show the decay rate of this probability in different dimensions.
ANNALS OF PROBABILITY
(2022)
Article
Statistics & Probability
Balazs Rath, Sandor Rokob
Summary: We introduce a new correlated percolation model called the random length worms model and investigate its connectivity properties. We provide a sufficient condition on the length distribution that guarantees percolation phase transition in this model for dimensions greater than or equal to 5. The percolative behavior of the random length worms model is shown to be close to extremal in a family of similar models.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Henrik Seckler, Ralf Metzler
Summary: Machine-learning techniques are used to decode anomalous-diffusion data and provide both predicted output and uncertainty estimates.
NATURE COMMUNICATIONS
(2022)
Article
Statistics & Probability
Adam M. Bowditch, David A. Croydon
Summary: This article studies the properties of biased random walk on the supercritical integer lattice. The research reveals that when the bias exponent is between (1, 2), the fluctuations of the random walk exhibit an anomalous polynomial order.
ELECTRONIC JOURNAL OF PROBABILITY
(2022)
Article
Mathematics, Applied
Florian Schweiger, Ofer Zeitouni
Summary: We study the distribution of the maximum of a class of Gaussian fields with logarithmic correlations and rare local defects. The centered maximum of the field asymptotically follows a randomly-shifted Gumbel distribution. We prove that the two dimensional Gaussian free field on a super-critical bond percolation cluster with p close enough to 1, as well as the Gaussian free field in i.i.d. bounded conductances, fall under the assumptions of our general theorem.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Jiri Cerny
Summary: This study considers the zero-average Gaussian free field on finite d-regular graphs with fixed d (greater than or equal to 3). This class includes d-regular expanders of large girth and typical realisations of random d-regular graphs. The study shows that the level set of the zero-average Gaussian free field above level h has a giant component in the whole supercritical phase.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Jeremie Brieussel, Tianyi Zheng
Summary: The study addresses the inverse problem of finite generated groups involving speed, entropy, isoperimetric profile, return probability, and L-p-compression functions. Additionally, it proves a recent conjecture related to joint evaluation of speed and entropy exponents and provides a new proof of the existence of uncountably many pairwise non-quasi-isometric solvable groups. Furthermore, a formula linking the L-p-compression exponent of a group and its wreath product with the cyclic group for p in [1, 2] is obtained.
ANNALS OF MATHEMATICS
(2021)
Article
Physics, Fluids & Plasmas
Zhenqi Lu, Johan Wahlstrom, Arye Nehorai
Summary: The study focuses on spreading phenomena in networks, especially disease transmission, and proposes a method to effectively contain and suppress epidemic outbreaks through a combination of antidote distribution and partial quarantine. By improving existing antidote distribution schemes based on personalized PageRank, the study shows that the probability of infection spreading to the whole network is bounded, and the infection inside the subnetwork will disappear after a period proportional to the logarithm of the initially infected nodes. The strategy is dependent only on infection rate, recovery rate, and the topology around initially infected nodes, regardless of the rest of the network.
Article
Physics, Fluids & Plasmas
Sheng Fang, Da Ke, Wei Zhong, Youjin Deng
Summary: We studied the backbone and shortest-path exponents of the two-dimensional Potts model using Monte Carlo simulations. Our results improve upon existing estimates and provide a more accurate understanding of the critical behavior of the model. The study also suggests an exact formula for the leading correction exponent.
Article
Computer Science, Information Systems
Kamal Berahmand, Elahe Nasiri, Saman Forouzandeh, Yuefeng Li
Summary: This article proposes an improved method for local random walk by encouraging the movement towards nodes with stronger influence, resulting in higher prediction accuracy. A comparison with other similarity-based methods was conducted on 11 real-world networks, and the results demonstrated its superior performance in link prediction.
JOURNAL OF KING SAUD UNIVERSITY-COMPUTER AND INFORMATION SCIENCES
(2022)
