Continuity and uniqueness of percolation critical parameters in finitary random interlacements
نویسندگان
چکیده
We prove that the critical percolation parameter for Finitary Random Interlacements (FRI) is continuous with respect to path length T. The proof uses a result which interesting on its own right; equality of natural parameters FRI phase transition.
منابع مشابه
ec adoption and critical success factors of ec in smes in iran
تجارت الکترونیکی شیوه اجرای مسئولیتها، تقابل با مشتریان و امور معمول عملیاتی در شرکتها را تغییر داده است. تجارت الکترونیکی در عمل تنها خرید و فروش کالاها را از طریق ابزار الکترونیک نمی باشد، بلکه تمام فعالیتهای لازم جهت انجام فرایند فروش را نیز در بر میگیرد. در اواخر دهه 1990 بسیاری از شرکتها فعالیتهای خود را به منظور دستیابی به مشتریان جدید و یا ارائه فرصتهای جدید به مشتریان موجود گسترش دادند...
Uniqueness and non-uniqueness in percolation theory
This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on Z d and, more generally, on transitive graphs. For iid percolation on Z, uniqueness of the infinite cluster is a classical result, while on certain other transitive graphs uniqueness may fail. Key properties of the graphs in this context turn out to be amenability ...
متن کاملLevel Set Percolation for Random Interlacements and the Gaussian Free Field
We consider continuous-time random interlacements on Z, d ≥ 3, and investigate the percolation model where a site x of Z is occupied if the total amount of time spent at x by all the trajectories of the interlacement at level u ≥ 0 exceeds some constant α ≥ 0, and empty otherwise. We also investigate percolation properties of empty sites. A recent isomorphism theorem [15] enables us to “transla...
متن کاملOn the Uniqueness of the Infinite Cluster of the Vacant Set of Random Interlacements
We consider the model of random interlacements on Z introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in u of the probability that the origin belongs to the infinite component of the vacant set at level u in the supercritical...
متن کاملDensity and Uniqueness in Percolation
Two results on site percolation on the d-dimensional lattice, d^l arbitrary, are presented. In the first theorem, we show that for stationary underlying probability measures, each infinite cluster has a well-defined density with probability one. The second theorem states that if in addition, the probability measure satisfies the finite energy condition of Newman and Schulman, then there can be ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2022
ISSN: ['1083-6489']
DOI: https://doi.org/10.1214/22-ejp824