Zur Meinungsbildung in einer heterogenen Bevölkerung – ein neuer Zugang zum Hopfield Modell

Knöpfel, Holger; Löwe, Matthias

doi:10.1007/s00591-008-0049-z

Cited by 4 publications

(3 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…in [17], [1], [28]. This latter approach follows very much the social re-interpretation for one group of the Curie-Weiss model in [6] or of the Hopfield model in [9] or [25]. A third source of interest in mean-field spin block models is a statistical point of view.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation Results for General Block Spin Ising Models

et al. 2020

Self Cite

View full text Add to dashboard Cite

We study a block spin mean-field Ising model. For the vector of block magnetizations we prove Large Deviation Principles and Central Limit Theorems under general assumptions for the block interaction matrix. Using the exchangeable pair approach of Stein's method we are also able to establish a speed of convergence for the Central Limit Theorem for the vector of block magnetizations in the high temperature regime.

show abstract

Section: Introductionmentioning

confidence: 99%

Fluctuation Results for General Block Spin Ising Models

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the 1990s and early 2000s interacting spins systems were discovered as a model for (mostly binary) discrete choice problems with social interaction, see e.g. [10], [17], [25], [13], [26], or [32]. From this list [10] is particularly interesting for our paper, because it gives a reinterpretation of the Curie-Weiss model from statistical physics in terms of discrete choice models with interactions.…”

Section: Introductionmentioning

confidence: 99%

Multi-group Binary Choice with Social Interaction and a Random Communication Structure -- a Random Graph Approach

Löwe,

Schubert,

Vermet

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We construct and analyze a random graph model for discrete choice with social interaction and several groups of equal size. We concentrate on the case of two groups of equal sizes and we allow the interaction strength within a group to differ from the interaction strength between the two groups. Given that the resulting graph is sufficiently dense we show that, with probability 1, the average decision in each of the two groups is the same as in the fully connected model. In particular, we show that there is a phase transition: If the interaction among a group and between the groups is strong enough the average decision per group will either be positive or negative and the decision of the two groups will be correlated. We also compute the free energy per particle in our model.

show abstract

“…Extensions of these models are studied in [19] or [21]. The first of these papers uses a very general interaction structure, while the latter investigates the situation in the spirit of social interaction models or statistical physics models on random graphs, see [23], [3], [7], and [18]. A related version of this model has been investigated using the method of moments in [15], [17] and [16].…”

Section: Introductionmentioning

confidence: 99%

Exact recovery in block spin Ising models at the critical line

Löwe¹,

Schubert²

2020

Electron. J. Statist.

Self Cite

View full text Add to dashboard Cite

We show how to exactly reconstruct the block structure at the critical line in the so-called Ising block model. This model was recently re-introduced by Berthet, Rigollet and Srivastavaz in [2]. There the authors show how to exactly reconstruct blocks away from the critical line and they give an upper bound on the number of observations one needs. Our technique relies on a combination of their methods with fluctuation results obtained in [20]. The latter are extended to the full critical regime. We find that the number of necessary observations depends on whether the interaction parameter between two blocks is positive or negative: In the first case, there are about N log N observations required to exactly recover the block structure, while in the latter √ N log N observations suffice.

show abstract

Zur Meinungsbildung in einer heterogenen Bevölkerung – ein neuer Zugang zum Hopfield Modell

Cited by 4 publications

References 32 publications

Fluctuation Results for General Block Spin Ising Models

Fluctuation Results for General Block Spin Ising Models

Multi-group Binary Choice with Social Interaction and a Random Communication Structure -- a Random Graph Approach

Exact recovery in block spin Ising models at the critical line

Contact Info

Product

Resources

About