2013/01/22 by Quentin Berger, Berger, Quentin
Mathematics · Physics and Astronomy · #60K37 #82B44 #82D60 #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K37 #msc:82B44 #msc:82D60
paper · pdf · doi:10.48550/arxiv.1301.5307
23 pages, 1 figure Modifications in v2 (outside minor typos): Assumption 1 on correlations has been simplified for more clarity; Theorem 4 has been improved to a more general underlying renewal distribution; Remark 2.1 added, on the assumption on the correlations in the summable case
openalex publication_date 2013/01/22 · arxiv created 2013/11/06 · arxiv updated 2013/11/07 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We study the random pinning model, in the case of a Gaussian environment presenting power-law decaying correlations, of exponent decay a>0. We comment on the annealed (i.e. averaged over disorder) model, which is far from being trivial, and we discuss the influence of disorder on the critical properties of the system. We show that the annealed critical exponent νann is the same as the homogeneous one νpur, provided that correlations are decaying fast enough (a>2). If correlations are summable (a>1), we also show that the disordered phase transition is at least of order 2, showing disorder relevance if νpur<2. If correlations are not summable (a<1), we show that the phase transition disappears.