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Random Growth Models
The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Introduction to Probability
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
A Course on Large Deviations with an Introduction to Gibbs Measures
This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course. The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. D...
Random Growth Models
The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course ""Random Growth Models"", held Ja.
Beyond AI, Blockchain Systems, and Digital Platforms
The ever-progressing digitalization of the economy and society is unlocking new opportunities for organizations engaging in services. We are in the middle of a transformation of the service sector that can be likened to the advent of mass production in the 1940s. Based on recent advances and developments in artificial intelligence, digital platforms, and blockchain systems, we are witnessing the emergence of new digitalization phenomena of metahuman systems, artificial intelligence platforms, and meta-organizations. Jointly, these forces are shaping now, or will be in the near future, the service activities of organizations around the world. They enable mass hyper-personalized services and m...
Informaatiosektorin energian- ja sähkönkäyttö Suomessa
The role of the digital technologies are becoming increasingly important in our day-to-day life. Digital technologies have become part of our social life as well as business operations across different industrial and public sectors. Because of digitalization the internet protocol and data traffic have been on the rise for several years. A few studies and estimates have been presented about the increasing future use of energy and electricity. Occasionally consumer behaviors have been claimed to be behind of these increases in electricity use.This report makes an effort to understand the energy and electricity consumption of the Finnish Information sector (ICT-sector) from 2011 until 2017. Additionally, we compare the Finnish electricity use to other Europe-an countries with similar data available. The findings of this study are partly inconsistent with those previously presented in terms of future energy and electricity use. Our report also shows that energy efficiencies of the information sector have not been retained while the internet protocol and data traffic have been increasing in both fixed and mobile networks.
Introduction to Probability
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
