The bi-dimensional Directed IDLA forest
نویسندگان
چکیده
We investigate three types of internal diffusion limited aggregation (IDLA) models. These models are based on simple random walks Z2 with infinitely many sources that the points vertical axis I(∞)={0}×Z. Various properties provided, such as stationarity, mixing, stabilization and shape theorems. Our results allow us to define a new directed (w.r.t. horizontal direction) forest spanning Z2, an IDLA protocol, which is invariant in distribution w.r.t. translations.
منابع مشابه
A simple FPRAS for bi-directed reachability
Gorodezky and Pak (Random Struct. Algorithms, 2014) introduced a “clusterpopping” algorithm for sampling root-connected subgraphs in a directed graph, and conjectured that it runs in expected polynomial time on bi-directed graphs. We confirm their conjecture. It follows that there is a fully polynomial-time randomized approximation scheme (FPRAS) for reachability in bi-directed graphs. Reachabi...
متن کاملImproved approximating algorithms for Directed Steiner Forest
We consider the k-Directed Steiner Forest (k-DSF) problem: given a directed graph G = (V,E) with edge costs, a collection D ⊆ V × V of ordered node pairs, and an integer k ≤ |D|, find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are...
متن کاملImproved approximation algorithms for Directed Steiner Forest
We consider the k-Directed Steiner Forest (k-DSF) problem: Given a directed graph G = (V,E) with edge costs, a collection D ⊆ V × V of ordered node pairs, and an integer k ≤ |D|, find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are...
متن کامل2-Dimensional Directed Type Theory
Recent work on higher-dimensional type theory has explored connections between Martin-Löf type theory, higher-dimensional category theory, and homotopy theory. These connections suggest a generalization of dependent type theory to account for computationally relevant proofs of propositional equality—for example, taking IdSet A B to be the isomorphisms between A and B. The crucial observation is...
متن کاملThe 2D-directed spanning forest is almost surely a tree
We consider the Directed Spanning Forest (DSF) constructed as follows: given a Poisson point process N on the plane, the ancestor of each point is the nearest vertex of N having a strictly larger abscissa. We prove that the DSF is actually a tree. Contrary to other directed forests of the literature, no Markovian process can be introduced to study the paths in our DSF. Our proof is based on a c...
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: Annals of Applied Probability
سال: 2023
ISSN: ['1050-5164', '2168-8737']
DOI: https://doi.org/10.1214/22-aap1865