scholarly journals Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees

2018 ◽  
Vol 173 (3-4) ◽  
pp. 1045-1081 ◽  
Author(s):  
Sander Dommers ◽  
Cristian Giardinà ◽  
Claudio Giberti ◽  
Remco van der Hofstad
Keyword(s):  
Ising Model ◽  
Large Deviations ◽  
Random Graphs ◽  
Inhomogeneous Random Graphs

scholarly journals Annealed central limit theorems for the Ising model on random graphs

2016 ◽  
Vol 13 (1) ◽  
pp. 1 ◽  
Author(s):  
C. Giardinà ◽  
C. Giberti ◽  
R. van der Hofstad ◽  
M. L. Prioriello
Keyword(s):  
Ising Model ◽  
Central Limit ◽  
Random Graphs ◽  
Limit Theorems ◽  
Central Limit Theorems

scholarly journals Big Jobs Arrive Early: From Critical Queues to Random Graphs

2020 ◽  
Vol 10 (4) ◽  
pp. 310-334
Author(s):  
Gianmarco Bet ◽  
Remco van der Hofstad ◽  
Johan S. H. van Leeuwaarden
Keyword(s):  
Head Start ◽  
Random Graphs ◽  
Queue Length ◽  
Busy Period ◽  
Asymptotic Result ◽  
Service Requirement ◽  
Exploration Process ◽  
Asymptotic Regime ◽  
Long Period ◽  
Inhomogeneous Random Graphs

We consider a queue to which only a finite pool of n customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement S arrives to the queue after an exponentially distributed time with mean S-α for some [Formula: see text]; therefore, larger service requirements trigger customers to join earlier. This finite-pool queue interpolates between two previously studied cases: α = 0 gives the so-called [Formula: see text] queue and α = 1 is closely related to the exploration process for inhomogeneous random graphs. We consider the asymptotic regime in which the pool size n grows to infinity and establish that the scaled queue-length process converges to a diffusion process with a negative quadratic drift. We leverage this asymptotic result to characterize the head start that is needed to create a long period of activity. We also describe how this first busy period of the queue gives rise to a critically connected random forest.

scholarly journals A two-populations Ising model on diluted random graphs

2010 ◽  
Vol 2010 (07) ◽  
pp. P07021 ◽  
Author(s):  
E Agliari ◽  
R Burioni ◽  
P Sgrignoli
Keyword(s):  
Ising Model ◽  
Random Graphs ◽  
Two Populations
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