?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F2262%2F&rft.title=Fluctuation+Theorems+for+Synchronization+of+Interacting+Polya's+urns&rft.creator=Crimaldi%2C+Irene&rft.creator=Dai+Pra%2C+Paolo&rft.creator=Minelli%2C+Ida+G.&rft.subject=HA+Statistics&rft.subject=QA+Mathematics&rft.description=We+consider+a+model+of+N+two-colors+urns+in+which+the+reinforcement+of+each+urn+depends+also+on+the+content+of+all+the+other+urns.+This+interaction+is+of+mean-field+type+and+it+is+tuned+by+a+parameter+%5Calpha+in+%5B0%2C1%5D%3B+in+particular%2C+for+%5Calpha%3D0+the+N+urns+behave+as+N+independent+Polya's+urns.+For+%5Calpha%3E0+urns+synchronize%2C+in+the+sense+that+the+fraction+of+balls+of+a+given+color+converges+a.s.+to+the+same+(random)+limit+in+all+urns.+In+this+paper+we+study+fluctuations+around+this+synchronized+regime.+The+scaling+of+these+fluctuations+depends+on+the+parameter+%5Calpha.+In+particular%2C+the+standard+scaling+t%5E%7B-1%2F2%7D+appears+only+for+%5Calpha%3E1%2F2.+For+%5Calpha%5Cgeq+1%2F2+we+also+determine+the+limit+distribution+of+the+rescaled+fluctuations.+We+use+the+notion+of+stable+convergence%2C+which+is+stronger+than+convergence+in+distribution.+&rft.date=2014-07&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Crimaldi%2C+Irene+and+Dai+Pra%2C+Paolo+and+Minelli%2C+Ida+G.++Fluctuation+Theorems+for+Synchronization+of+Interacting+Polya's+urns.++Technical+Report+++++++(Submitted)+++&rft.relation=http%3A%2F%2Farxiv-web3.library.cornell.edu%2Fabs%2F1407.5043%3Fcontext%3Dmath