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تسجيل مستخدم جديدUniversality and Sharpness in Absorbing-State Phase Transitions
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We consider the Activated Random Walk model in any dimension with any sleep rate and jump distribution and ergodic initial state. We show that the stabilization properties depend only on the average density of particles, regardless of how they are initially located on the lattice.
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Consider $Ntimes N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W geq N^{3/4+varepsilon}$ for any $varepsilon>0$. In the bulk of the spectrum and in the large $N$ limit, we obtain the foll
owing results. (i) The semicircle law holds up to the scale $N^{-1+varepsilon}$ for any $varepsilon>0$. (ii) The eigenvalues locally converge to the point process given by the Gaussian orthogonal ensemble at any fixed energy. (iii) All eigenvectors are delocalized, meaning their ${rm L}^infty$ norms are all simultaneously bounded by $N^{-frac{1}{2}+varepsilon}$ (after normalization in ${rm L}^2$) with overwhelming probability, for any $varepsilon>0$. (iv )Quantum unique ergodicity holds, in the sense that the local ${rm L}^2$ mass of eigenvectors becomes equidistributed with overwhelming probability. We extend the mean-field reduction method cite{BouErdYauYin2017}, which required $W=Omega(N)$, to the current setting $W ge N^{3/4+varepsilon}$. Two new ideas are: (1) A new estimate on the generalized resolvent of band matrices when $W geq N^{3/4+varepsilon}$. Its proof, along with an improved fluctuation average estimate, will be presented in parts 2 and 3 of this series cite {BouYanYauYin2018,YanYin2018}. (2) A strong (high probability) version of the quantum unique ergodicity property of random matrices. For its proof, we construct perfect matching observables of eigenvector overlaps and show they satisfying the eigenvector moment flow equation cite{BouYau2017} under the matrix Brownian motions.
The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization group, it is shown that for any amount of disorder the critical be
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We consider a class of nonlinear mappings $mathsf{F}_{A,N}$ in $mathbb{R}^N$ indexed by symmetric random matrices $Ainmathbb{R}^{Ntimes N}$ with independent entries. Within spin glass theory, special cases of these mappings correspond to iterating th
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We consider a simple discrete-time Markov chain with values in $[0,infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary contact pa
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