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Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity

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Release : 2023-09-27
Genre : Mathematics
Kind : eBook
Book Rating : 996/5 ( reviews)

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Book Synopsis Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity by : Olivier Bernardi

Download or read book Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity written by Olivier Bernardi. This book was released on 2023-09-27. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation

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Release : 2024-02-01
Genre : Mathematics
Kind : eBook
Book Rating : 917/5 ( reviews)

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Book Synopsis Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation by : Erik Bates

Download or read book Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation written by Erik Bates. This book was released on 2024-02-01. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Peeling Random Planar Maps

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Release : 2023-11-20
Genre : Mathematics
Kind : eBook
Book Rating : 541/5 ( reviews)

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Book Synopsis Peeling Random Planar Maps by : Nicolas Curien

Download or read book Peeling Random Planar Maps written by Nicolas Curien. This book was released on 2023-11-20. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walks, self-avoiding random walks...). A “Markovian” approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes. This technique, known as "peeling exploration" in the literature, can be seen as a generalization of the well-known coding processes for random trees (e.g. breadth first or depth first search). It is revealed that different types of Markovian explorations can yield different types of information about a surface. Based on an École d'Été de Probabilités de Saint-Flour course delivered by the author in 2019, the book is aimed at PhD students and researchers interested in graph theory, combinatorial probability and geometry. Featuring open problems and a wealth of interesting figures, it is the first book to be published on the theory of random planar maps.

Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity

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Release : 2024-01-19
Genre : Mathematics
Kind : eBook
Book Rating : 680/5 ( reviews)

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Book Synopsis Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity by : Mathias Pétréolle

Download or read book Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity written by Mathias Pétréolle. This book was released on 2024-01-19. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity

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Release : 2024-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 778/5 ( reviews)

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Book Synopsis Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity by : Roberto Feola

Download or read book Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity written by Roberto Feola. This book was released on 2024-04-17. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

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