ﻻ يوجد ملخص باللغة العربية
Let $T$ be a random ergodic pseudometric over $mathbb R^d$. This setting generalizes the classical emph{first passage percolation} (FPP) over $mathbb Z^d$. We provide simple conditions on $T$, the decay of instant one-arms and exponential quasi-independence, that ensure the positivity of its time constants, that is almost surely, the pseudo-distance given by $T$ from the origin is asymptotically a norm. Combining this general result with previously known ones, we prove that The known phase transition for Gaussian percolation in the case of fields with positive correlations with exponentially fast decayholds for Gaussian FPP, including the natural Bargmann-Fock model; The known phase transition for Voronoi percolation also extends to the associated FPP; The same happens for Boolean percolation for radii with exponential tails, a result which was known without this condition. We prove the positivity of the constant for random continuous Riemannian metrics, including cases with infinite correlations in dimension $d=2$. Finally, we show that the critical exponent for the one-arm, if exists, is bounded above by $d-1$. This holds forbond Bernoulli percolation, planar Gaussian fields, planar Voronoi percolation, and Boolean percolation with exponential small tails.
We prove a non-asymptotic concentration inequality for the spectral norm of sparse inhomogeneous random tensors with Bernoulli entries. For an order-$k$ inhomogeneous random tensor $T$ with sparsity $p_{max}geq frac{clog n}{n }$, we show that $|T-mat
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching structure. F
We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences. Applications to random dynamical systems and diffusions are studied.
We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of homogenization for Dyson Brownian Motion, this yields the universality of quantities which depend on the behavior
A classical result for the simple symmetric random walk with $2n$ steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the maximum height all have exactly the same distribution and converge whe