Percolation models 9/9 - Oriented site percolation and forest fire model.
Assume that trees in a forest are distributed according to a two-dimensional Poisson point process. Start with one burning tree and assume that all the trees within distance one of a burning tree start burning forever. In this video, we use results from percolation theory to prove that the probability of an infinite fire is zero when the intensity is small and positive when the intensity is large. This is Exercises 9.2 and 13.6 of my Stochastic Modeling book.
This video is part of the playlist Stochastic Modeling https://www.youtube.com/watch?v=DWP7_Pvxync&list=PLV3oHJg9b1NRKMFQ_XGzBmj4J7vASnBfG
Видео Percolation models 9/9 - Oriented site percolation and forest fire model. канала The probability channel - Professor Lanchier
This video is part of the playlist Stochastic Modeling https://www.youtube.com/watch?v=DWP7_Pvxync&list=PLV3oHJg9b1NRKMFQ_XGzBmj4J7vASnBfG
Видео Percolation models 9/9 - Oriented site percolation and forest fire model. канала The probability channel - Professor Lanchier
Показать
Комментарии отсутствуют
Информация о видео
3 сентября 2020 г. 5:57:10
00:30:28
Другие видео канала
Combinatorial analysis 4/13 (exercise 1.11) - Permutations without repetition 2.
Conditional probability 5/10 (exercise 3.43) - Bayes' formula with three coins.
Continuous-time Markov chains - Existence of a stationary distribution example (queueing system).
Continuous random variables 6/9 (exercise 5.32) - Memoryless property of the exponential.
Joint distribution 11/11 (exercise 6.12) - Poisson: thinning property.
Continuous-time Markov chains 7/15 - Convergence theory: daily profit of a barbershop.
Discrete-time Markov chains 7/21 - Recurrence and transience: 2D random walk.
Axioms of probability 11/12 (exercise 2.12) - Inclusion-exclusion and Venn diagrams.
Discrete-time Markov chains 14/21 - Mean recurrence time: time between movies.
Discrete random variables 5/13 (exercise 4.20) - Winning strategy at the game of roulette?
Stochastic models in biology 1/9 - Introduction and playlist overview.
Discrete random variables 7/13 - Binomial and geometric, Poisson and exponential.
Stochastic simulations 1/12 - Introduction and playlist overview.
Combinatorial analysis 9/13 (exercise 1.27) - Permutations with repetition 2.
Stochastic models in biology 8/9 - Wright-Fisher model and Kingman's coalescent.
Stochastic simulations 2/12 - How to simulate discrete random variables?
Conditional probability 4/10 (exercise 3.37) - Bayes' formula with two coins.
Conditional probability 6/10 (exercise 3.22) - Probability of an ordering of three dice.
Discrete random variables 8/13 (exercise 4.40) - Binomial and multiple choice exam.
Stochastic simulations 11/12 - How to simulate the contact process?