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"The name "random walk" for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of "Nature". The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier such a problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays the theory of random walks has proved useful in physics and chemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcellular structures) and in many other disciplines. The random walk approach serves not only as a model of simple diffusion but of many complex sub- and super-diffusive transport processes as well. This book discusses the main variants of random walks and gives the most important mathematical tools for their theoretical description"--

Random walks (Mathematics) --- Additive process (Probability theory) --- Random walk process (Mathematics) --- Walks, Random (Mathematics) --- Stochastic processes

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Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.

Random walks (Mathematics) --- Diffusion processes. --- Markov processes. --- Charts, diagrams, etc. --- Diagrams, charts, etc. --- Graphs --- Plots (Diagrams) --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Markov processes --- Additive process (Probability theory) --- Random walk process (Mathematics) --- Walks, Random (Mathematics) --- Cell aggregation --- Data structures (Computer scienc. --- Engineering. --- Applications of Graph Theory and Complex Networks. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Data Structures and Information Theory. --- Complexity. --- Mathematics. --- Construction --- Industrial arts --- Technology --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Data structures (Computer science) --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Physics. --- Manifolds (Mathematics). --- Complex manifolds. --- Data structures (Computer science). --- Computational complexity. --- Complexity, Computational --- Machine theory --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics