000171390 001__ 171390
000171390 005__ 20180913060938.0
000171390 0247_ $$2doi$$a10.1007/s00440-010-0266-y
000171390 02470 $$2ISI$$a000290725200002
000171390 037__ $$aARTICLE
000171390 245__ $$aLyapunov exponents of Green's functions for random potentials tending to zero
000171390 269__ $$a2011
000171390 260__ $$c2011
000171390 336__ $$aJournal Articles
000171390 520__ $$aWe consider quenched and annealed Lyapunov exponents for the Green's function of -Delta + gamma V, where the potentials V(x) ,x epsilon Z(d), are i.i.d. nonnegative random variables and gamma > 0 is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like root gamma as gamma tends to 0. Here the constant c is the same for the quenched as for the annealed exponent and is computed explicitly. This improves results obtained previously by Wang. We also consider other ways to send the potential to zero than multiplying it by a small number.
000171390 6531_ $$aAnnealed
000171390 6531_ $$aGreen's function
000171390 6531_ $$aLyapunov exponent
000171390 6531_ $$aQuenched
000171390 6531_ $$aRandom potential
000171390 6531_ $$aRandom walk
000171390 6531_ $$aRandom-Walks
000171390 6531_ $$aBounds
000171390 6531_ $$aZ(D)
000171390 700__ $$aKosygina, Elena$$uBaruch Coll, Dept Math, New York, NY 10010 USA
000171390 700__ $$0244703$$aMountford, Thomas S.$$g138859$$uEcole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne, Switzerland
000171390 700__ $$aZerner, Martin P. W.$$uUniv Tubingen, Math Inst, D-72076 Tubingen, Germany
000171390 773__ $$j150$$q43-59$$tProbability Theory And Related Fields
000171390 909C0 $$0252347$$pPRST$$xU10128
000171390 909CO $$ooai:infoscience.tind.io:171390$$pSB$$particle
000171390 937__ $$aEPFL-ARTICLE-171390
000171390 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000171390 980__ $$aARTICLE