Random walks on disordered media and their scaling limits : École d'Été de Probabilités de Saint-Flour XL-2010 /
Kumagai, Takashi, 1967-
Random walks on disordered media and their scaling limits : École d'Été de Probabilités de Saint-Flour XL-2010 / École d'Été de Probabilités de Saint-Flour XL-2010 Takashi Kumagai. - 1 online resource (x, 147 pages) : illustrations - Lecture notes in mathematics, 2101 1617-9692 ; . - Lecture notes in mathematics (Springer-Verlag) ; 2101. .
Includes bibliographical references (pages 135-143) and index.
Introduction -- Weighted graphs and the associated Markov chains -- Heat kernel estimates -- General theory -- Heat kernel estimates using effective resistance -- Heat kernel estimates for random weighted graphs -- Alexander-Orbach conjecture holds when two-point functions behave nicely -- Further results for random walk on IIC -- Random conductance model.
In these lecture notes, we will analyze the behavior of random walk on disordered mediaby means ofboth probabilistic and analytic methods, and will study the scalinglimits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. Thefirst few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has beensignificantprogress on thetheoryof random walkon disordered media such as fractals and random media. Random walk on a percolation cluster('the ant in the labyrinth')is one of the typical examples. In 1986, H. Kesten showedtheanomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.
English.
9783319031521 331903152X
10.1007/978-3-319-03152-1 doi
Springer
016636128 Uk
Random walks (Mathematics)
Marches aléatoires (Mathématiques)
Recorridos aleatorios (Matemáticas)
Random walks (Mathematics)
QA274.73
519.2
Random walks on disordered media and their scaling limits : École d'Été de Probabilités de Saint-Flour XL-2010 / École d'Été de Probabilités de Saint-Flour XL-2010 Takashi Kumagai. - 1 online resource (x, 147 pages) : illustrations - Lecture notes in mathematics, 2101 1617-9692 ; . - Lecture notes in mathematics (Springer-Verlag) ; 2101. .
Includes bibliographical references (pages 135-143) and index.
Introduction -- Weighted graphs and the associated Markov chains -- Heat kernel estimates -- General theory -- Heat kernel estimates using effective resistance -- Heat kernel estimates for random weighted graphs -- Alexander-Orbach conjecture holds when two-point functions behave nicely -- Further results for random walk on IIC -- Random conductance model.
In these lecture notes, we will analyze the behavior of random walk on disordered mediaby means ofboth probabilistic and analytic methods, and will study the scalinglimits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. Thefirst few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has beensignificantprogress on thetheoryof random walkon disordered media such as fractals and random media. Random walk on a percolation cluster('the ant in the labyrinth')is one of the typical examples. In 1986, H. Kesten showedtheanomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.
English.
9783319031521 331903152X
10.1007/978-3-319-03152-1 doi
Springer
016636128 Uk
Random walks (Mathematics)
Marches aléatoires (Mathématiques)
Recorridos aleatorios (Matemáticas)
Random walks (Mathematics)
QA274.73
519.2