ترغب بنشر مسار تعليمي؟ اضغط هنا

An invariance principle for one-dimensional random walks among dynamical random conductances

141   0   0.0 ( 0 )
 نشر من قبل Biskup Marek
 تاريخ النشر 2018
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Marek Biskup




اسأل ChatGPT حول البحث

We study variable-speed random walks on $mathbb Z$ driven by a family of nearest-neighbor time-dependent random conductances ${a_t(x,x+1)colon xinmathbb Z, tge0}$ whose law is assumed invariant and ergodic under space-time shifts. We prove a quenched invariance principle for the random walk under the minimal moment conditions on the environment; namely, assuming only that the conductances possess the first positive and negative moments. A novel ingredient is the representation of the parabolic coordinates and the corrector via a dual random walk which is considerably easier to analyze.



قيم البحث

اقرأ أيضاً

Consider a system of particles performing nearest neighbor random walks on the lattice $ZZ$ under hard--core interaction. The rate for a jump over a given bond is direction--independent and the inverse of the jump rates are i.i.d. random variables be longing to the domain of attraction of an $a$--stable law, $0<a<1$. This exclusion process models conduction in strongly disordered one-dimensional media. We prove that, when varying over the disorder and for a suitable slowly varying function $L$, under the super-diffusive time scaling $N^{1 + 1/alpha}L(N)$, the density profile evolves as the solution of the random equation $partial_t rho = mf L_W rho$, where $mf L_W$ is the generalized second-order differential operator $frac d{du} frac d{dW}$ in which $W$ is a double sided $a$--stable subordinator. This result follows from a quenched hydrodynamic limit in the case that the i.i.d. jump rates are replaced by a suitable array ${xi_{N,x} : xinbb Z}$ having same distribution and fulfilling an a.s. invariance principle. We also prove a law of large numbers for a tagged particle.
We study models of continuous time, symmetric, $Z^d$-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We consider t he case of independent conductances with a polynomial tail near 0, and obtain precise asymptotics for the annealed return probability and convergence times for the random walk confined to a finite box.
We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of valleys of height $log t$. In t he quenched setting, we also sharply estimate the distribution of the walk at time $t$.
151 - Yueyun Hu , Nobuo Yoshida 2007
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d ge 3$ and the environment is not too random, then, the total population gro ws as fast as its expectation with strictly positive probability. If,on the other hand, $d le 2$, or the environment is ``random enough, then the total population grows strictly slower than its expectation almost surely. We show the equivalence between the slow population growth and a natural localization property in terms of replica overlap. We also prove a certain stronger localization property, whenever the total population grows strictly slower than its expectation almost surely.
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We study the p robability that the random walk travels slower than its typical speed and determine its decay rate asymptotic.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا