On mesoscopic equilibrium for linear statistics in Dyson's Brownian motion / / Maurice Duits, Kurt Johansson

• Record Nr.: UNINA9910478891903321
• Autore: Duits Maurice
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2018]; ©2018
• ISBN: 1-4704-4821-1
• Descrizione fisica: 1 online resource (130 pages)
• Collana: Memoirs of the American Mathematical Society ; ; Volume 255, Number 1222
• Disciplina: 519.2/33
• Soggetti: Stochastic processes; Stochastic differential equations; Mesoscopic phenomena (Physics); Brownian motion processes; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Statement of results -- 2.1. Assumptions on ⱼ⁽ⁿ⁾ -- 2.2. Deterministic initial points -- 2.3. Concentration inequalities -- 2.4. Random initial points -- 2.5. Further remarks -- 2.6. Overview of the rest of the paper -- Chapter 3. Proof of Theorem 2.1 -- 3.1. Determinantal strucure -- 3.2. Asymptotic results for _{ } and _{ }^{ } -- 3.3. Proof of Theorem 2.1 -- Chapter 4. Proof of Theorem 2.3 -- 4.1. Overview of the proof -- 4.2. The loop equations -- 4.3. Loop equations on the mesoscopic scale -- 4.4. Proof of Theorem 2.3 -- Chapter 5. Asymptotic analysis of _{ } and _{ } -- 5.1. Integrable form of _{ } -- 5.2. The functions ℰⱼ -- 5.3. Saddle points -- 5.4. Deforming the contours -- 5.5. Asymptotics for ⱼ and ⱼ -- 5.6. Proof of Lemma 3.2 -- 5.7. Asymptotics for _{ }( , ) -- 5.8. Asymptotics for ^{ }_{ } -- Chapter 6. Proof of Proposition 2.4 -- 6.1. Preliminaries -- 6.2. A first concentration inequality -- 6.3. Proof of Poposition 6.2 -- 6.4. A concentration inequality using the logaritmic Sobolev inequality -- 6.5. Proof of Proposition 2.4 -- 6.6. One more concentration inequality -- ; Chapter 7. Proof of Lemma 4.3 -- 7.1. Preliminaries -- 7.2. Estimating _{ }^{ _{ }^{\eps}} -- 7.3. Estimating _{ }^{ _{ }^{\eps}} -- 7.4. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1/2 -- 7.5. Estimating ^{ _{ }^{\eps}}_{ } for 0< <1 -- Chapter 8. Random initial points -- 8.1. Preliminary lemmas -- 8.2. Regularity of the initial points -- 8.3. Smoothening the test function -- 8.4. Approximating _{ }( ) -- 8.5. Proof of Theorem 2.5, and Theorem 2.6 with the assumption ₀( )≠0 -- Chapter 9. Proof of Theorem 2.6: the general case -- 9.1. Smoothening of the test function -- 9.2. Change of variables -- 9.3. Expansion into moments.; 9.4. Proof of Proposition 9.1 -- 9.5. Proof of Theorem 2.6: the general case -- Appendix -- Bibliography -- Back Cover.
• Sommario/riassunto: In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with \beta =2. Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.

Advances in Social Simulation : Proceedings of the 16th Social Simulation Conference, 20–24 September 2021 / / edited by Marcin Czupryna, Bogumił Kamiński

• Record Nr.: UNINA9910558491803321
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
• ISBN: 3-030-92843-8
• Edizione: [1st ed. 2022.]
• Descrizione fisica: 1 online resource (463 pages)
• Collana: Springer Proceedings in Complexity, , 2213-8692
• Disciplina: 300.285; 300.113
• Soggetti: System theory; Computational complexity; Mathematical physics; Computer simulation; Psychology; Complex Systems; Computational Complexity; Computational Physics and Simulations; Behavioral Sciences and Psychology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Efficient Redistribution of Scarce Resources Favours Hierarchies -- Evaluation of COVID-19 Infection Prevention Measures Compatible with Local Economy -- DIPP: Diffusion of Privacy Preferences in Online Social Networks -- Explaining and Resolving Norm-behavior Inconsistencies – A Theoretical Agent-based Model -- Towards More Realism in Pedestrian Behaviour Models First Steps and Considerations in Formalising Social Identity -- Developing a Stakeholder-centric Simulation Tool to Support Integrated Mobility Planning -- Support Local Empowerment Using Various Modeling Approaches and Model Purposes: a Practical and Theoretical Point of View -- Exploring Coevolutionary Dynamics Between Infinitely Diverse Heterogenous Adaptive Automated Trading Agents -- Pay-for-Performance and ; Emerging Search Behavior: When Exploration Serves to Reduce Alterations -- Effects of Limited and Heterogeneous Memory in Hidden-action Situations -- Autonomous Group Formation of Heterogeneous Agents in Complex Task Environments -- Exploring Regional Agglomeration Dynamics in Face of Climate-driven Hazards: Insights from an Agent-based Computational Economic Model -- Dynamics of Wealth Inequality in Simple Artificial Societies -- Cruising Drivers' Response to Changes in Parking Prices in a Serious Game -- Quantum Leaper : A Methodology Journey From a Model in NetLogo to a Game in Unity -- How Perceived Complexity Impacts on Comfort Zones in Social Decision Contexts - Combining Gamification and Simulation for Assessment -- A Hybrid Agent-based Model to Simulate and Re-think Post-COVID-19 Use Processes in Educational Facilities -- Generation Gaps: An Agent-Based Model of Opinion Shifts among Cohorts -- Comparison of Viral Information Spreading Strategies in Social Media -- An Evidence-Driven Model of Voting and Party Competition -- Shrinking Housing’sSize Using Agent-based Modelling to Explore Measures for a Reduction of Floor Area per Capita -- The Problem with Bullying: Lessons Learned from Modelling Marginalization with Diverse Stakeholders -- On the Impact of Misvaluation on Bilateral Trading -- Consumer Participation in Demand Response Programs: Development of a Consumat-based Toy Model -- Using MBTI Agents to Simulate Human Behavior in a Work Context.
• Sommario/riassunto: This book covers the latest advances in applying agent-based modelling in social sciences. The Social Simulation Conference is the major global conference devoted to this topic. It is aimed at promoting social simulation and computational social science. This year’s special theme is “Social Simulation geared towards Post-Pandemic times”, focused not only on questions raised by the current pandemic but also on future challenges related to economic recovery, such as localization, globalization, inequality, sustainable growth and social changes induced by progressive digitalization, data availability and artificial intelligence. The primary audience of this book are scholars and practitioners in computational social sciences including economics, business, sociology, politics, psychology and urban studies.