Stochastic Opinion Dynamics: Theory and Application

1 Introduction
1.1 Motivation and Background
1.2 Outline of the Book
References
2 Preliminaries
2.1 Basic Definitions
2.2 Main Theorems
References
3 Homogeneous HK Model in Bounded Space
3.1 HK Models
3.2 Critical Noise for Quasi-Consensus
3.3 Sufficient Condition for Quasi-Consensus
3.4 Necessary Condition for Quasi-Consensus
3.5 Simulations
3.6 Notes
References
4 Homogeneous HK Model in Unbounded Space
4.1 Model and Definitions
4.2 Main Results
4.3 Simulations
4.4 Notes
References
5 Heterogeneous HK Model with Environment and Communication Noise
5.1 Models and Definitions
5.1.1 Heterogeneous Mode]s with Environment Noise
5.1.2 Heterogeneous Models with Communication Noise
5.1.3 Definitions
5.2 Main Results for Quasi-Synchronization
5.2.1 Proofs of Theorems 5. l and 5.2, and Corollaries 5.1 and 5.2
5.2.2 Proofs of Theorems 5.3 and 5.4
5.3 Increasing Confidence Thresholds May Harm Synchronization under System (5.3)
5.4 Notes
References
6 Random Information Flow Benefits Truth Seeking
6.1 Preliminary and Formulation
6.1.1 Truth Seeking Model
6.1.2 Free Information Flow
6.1.3 Approach Truth
6.2 Main Results
6.3 Simulations
6.4 Notes
References
7 Elimination of Disagreement via Covert Noise
7.1 Preliminaries and Formulation
7.1.1 HK-Based Divisive System
7.1.2 Noise Intervened System
7.1.3 ¦Õ-Consensus
7.2 ¦Õ-Consensus of Noise-Intervened System
7.3 soft Control Strategy
7.4 Stopping Time of Reaching 0-Consensus
7.5 Simulations
7.6 Notes
References
8 Robust Fragmentation of HK-Type Dynamics
8.1 ¦Õ-Consensus of HK-Type Models
8.1.1 Noisy HK-Type Models
8.1.2 6-Consensus
8.1.3 Spontaneous ¦Õ-Consensus Caused by Noise
8.2 HK Model with Heterogenous Prejudices
8.3 Simulations
8.4 Notes
References
Appendix A Proofs
A.1 Proof of Lemma 5.2
A.2 Proof of Lemma 5.3
A.3 Proof of Lemma 5.4
A.4 Proof of Lemma 5.5
A.5 Proof of Lemma 5.8
A.6 Proof of Lemma 5.9
A.7 Proof of Lemma 5.10
A.8 Proof of Lemma 5.11
A.9 Proof of Lemma 5.12