Geodesics In Random Growth Models
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Geodesics In Random Growth Models
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Author : Xiao Shen
language : en
Publisher:
Release Date : 2021
Geodesics In Random Growth Models written by Xiao Shen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
We study two percolation-type models related to the Kardar-Parisi-Zhang (KPZ) universality class: first-passage percolation (FPP) and exponential corner growth model (CGM). FPP is one of the famous conjectural members of the KPZ class, on the other hand, the CGM is one of its important integrable members. In both models, growth proceeds along optimal paths called geodesics, determined by a random environment. In a joint work with Timo Seppalainen, we establish estimates for the coalescence time of semi-infinite directed geodesics in CGM. There are four estimates: upper and lower bounds on the probabilities of both fast and slow coalescence on the correct spatial scale with exponent 3/2. Our proofs utilize a geodesic duality introduced by Pimentel and properties of the increment-stationary last-passage percolation process. For fast coalescence our bounds are new and they have a matching optimal exponential order of magnitude. For slow coalescence we reproduce bounds proved earlier with integrable probability inputs, except that our upper bound misses the optimal order by a logarithmic factor. In a joint work with Michael Damron, Chris Janjigian and Wai-Kit Lam, we establish tail estimates for the averaged empirical distribution of edge weights along geodesics in first-passage percolation in general dimensions. As an application, we show that if the edge weight distribution has finite positive moments of any order, then any limit point of the averaged empirical distribution of finite geodesics has finite positive moments of all orders.
Random Growth Models
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Author : Michael Damron
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-27
Random Growth Models written by Michael Damron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Random measures categories.
The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Random Graph And Growth Models
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Author :
language : en
Publisher:
Release Date : 2020
Random Graph And Growth Models written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
In And Out Of Equilibrium 3 Celebrating Vladas Sidoravicius
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Author : Maria Eulália Vares
language : en
Publisher: Springer Nature
Release Date : 2021-03-25
In And Out Of Equilibrium 3 Celebrating Vladas Sidoravicius written by Maria Eulália Vares and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-25 with Mathematics categories.
This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.
Brownian Regularity For The Airy Line Ensemble And Multi Polymer Watermelons In Brownian Last Passage Percolation
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Author : Alan Hammond
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-24
Brownian Regularity For The Airy Line Ensemble And Multi Polymer Watermelons In Brownian Last Passage Percolation written by Alan Hammond and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-24 with Mathematics categories.
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Probability On Discrete Structures
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Author : Harry Kesten
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Probability On Discrete Structures written by Harry Kesten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
Random Walks On Infinite Groups
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Author : Steven P. Lalley
language : en
Publisher: Springer Nature
Release Date : 2023-05-08
Random Walks On Infinite Groups written by Steven P. Lalley and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-08 with Mathematics categories.
This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.
Innovations For Shape Analysis
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Author : Michael Breuß
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-04
Innovations For Shape Analysis written by Michael Breuß and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-04 with Mathematics categories.
The concept of 'shape' is at the heart of image processing and computer vision, yet researchers still have some way to go to replicate the human brain's ability to extrapolate meaning from the most basic of outlines. This volume reflects the advances of the last decade, which have also opened up tough new challenges in image processing. Today's applications require flexible models as well as efficient, mathematically justified algorithms that allow data processing within an acceptable timeframe. Examining important topics in continuous-scale and discrete modeling, as well as in modern algorithms, the book is the product of a key seminar focused on innovations in the field. It is a thorough introduction to the latest technology, especially given the tutorial style of a number of chapters. It also succeeds in identifying promising avenues for future research. The topics covered include mathematical morphology, skeletonization, statistical shape modeling, continuous-scale shape models such as partial differential equations and the theory of discrete shape descriptors. Some authors highlight new areas of enquiry such as partite skeletons, multi-component shapes, deformable shape models, and the use of distance fields. Combining the latest theoretical analysis with cutting-edge applications, this book will attract both academics and engineers.
Growth And Geodesics Of Thompson S Group F
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Author : Jennifer L. Schofield
language : en
Publisher:
Release Date : 2009
Growth And Geodesics Of Thompson S Group F written by Jennifer L. Schofield and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Electronic dissertations categories.
In this paper our goal is to describe how to find the growth of Thompson's group F with generators a and b. Also, by studying elements through pipe systems, we describe how adding a third generator c affects geodesic length. We model the growth of Thompson's group F by producing a grammar for reduced pairs of trees based on Blake Fordham's tree structure. Then we change this grammar into a system of equations that describes the growth of Thompson's group F and simplify. To complete our second goal, we present and discuss a computer program that has led to some discoveries about how generators affect the pipe systems. We were able to find the growth function as a system of 11 equations for generators a and b.
Medical Image Computing And Computer Assisted Intervention Miccai 2011
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Author : Gabor Fichtinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-02
Medical Image Computing And Computer Assisted Intervention Miccai 2011 written by Gabor Fichtinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-02 with Computers categories.
The three-volume set LNCS 6891, 6892 and 6893 constitutes the refereed proceedings of the 14th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2011, held in Toronto, Canada, in September 2011. Based on rigorous peer reviews, the program committee carefully selected 251 revised papers from 819 submissions for presentation in three volumes. The second volume includes 83 papers organized in topical sections on diffusion weighted imaging, fMRI, statistical analysis and shape modeling, and registration.