Random Walks and Diffusion Assignment Homework Help

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The team has helped a number of students in Random Walks & Diffusion pursuing education through regular and online universities, institutes or online Tutoring in the following topics:

  • Additive versus Multiplicative Processes
  • Additivity of Tail Amplitudes
  • Application to Flagellar Bacteria
  • Applications of Conformal Mapping
  • Asymptotic Analysis Leading to Edgeworth Expansions
  • Asymptotics of Rayleigh's Random Walk, Central Limit Theorem
  • Burgers' Equation Surface Growth
  • Central Limit Theorem the Diffusion Equation
  • Cole Hopf Transformation, General Solution of Burgers Equation
  • Comparison of Discrete and Continuous Dynamics
  • Computer Simulation of Pearson's Random Walk to find the Fraction of Time Spent in the Right Half Plane ("Arcsine Law") and the First Quadrant
  • Computer Simulation of the Winding Angle for Pearson's Random Walk, Logarithmic Scaling and Limiting Distribution
  • Concentration dependent Diffusion, Chemical Potential Rechargeable Batteries, Steric Effects
  • Concentration-dependent Drift Nonlinear Waves in Traffic Flow
  • Conformal Invariance of the Hitting Probability
  • Conformal Transformations Conformally Invariant Transport Processes
  • Continuum Derivation Involving the Diffusion Equation
  • Continuum Limit of Bouchaud-Sornette Theory for Options with Residual Risk
  • Creeper Examples: Levy Walks, Bacterial Motion, Turbulent Dispersion
  • Derivation of the Discrete Arcsine Distribution for the Fraction of Time Spent on One Side of the Origin
  • Diffusion-limited Aggregation
  • Discrete Versus Continuous Stochastic Processes
  • Distribution for the Fraction of Time Spent on One Side of the Origin, Continuum Limit
  • Diverging Moments and Singular Characteristic Functions
  • Diverging Moments Singular Characteristic Functions
  • Electrostatic Analogy for Diffusion, First Passage to a Sphere
  • Eventual Hitting Probability, Electrostatic Analogy for Diffusion
  • Exact Green Function
  • Exact Similarity Solutions for Parabolic Flow to a Point Orifice
  • Fat Tails Riesz Fractional Derivatives
  • Financial Time Series
  • First Passage Return on a Lattice
  • Fokker-Planck Equation
  • General Formulation in Higher Dimensions
  • Global Accuracy and Fast Convergence of the Asymptotic Approximation
  • Globally-valid Saddle-point Asymptotics for a Random Walk with Exponentially Distributed Displacements
  • Governing Convergence to the CLT and more Generally Gram-Charlier Expansions for Random Walks
  • Gram-Charlier Expansion
  • Green-Kubo Relation, Persistence Length, Telegrapher's Equation
  • Harmonic Measure, Hastings Levitov Algorithm, Comparison of Discrete Continuous Dynamics
  • Hastings-Levitov Algorithm
  • Hughes' Leaper Creeper Models
  • Interacting Random Walkers
  • Interpretation as Risk Neutral Valuation, Put-call Parity
  • Kardar-Parisi-Zhang Equation Nonlinear Diffusion
  • Kramers-Moyall Expansion
  • Laplace Transform. Renewal Theory
  • Large Steps Versus Long Waiting Times
  • Law of the iterated logarithm
  • Leapers Creepers
  • Lévy flight foraging hypothesis
  • Linear Polymer Structure
  • Loop-erased random walk
  • Markov Chain for the Position
  • Mechanisms for Anomalous Diffusion Non identical Steps
  • Method of Steepest Descent for Asymptotic Approximation of Integrals
  • Minimum First Passage Time of a Set of N Random Walkers
  • Mittag-Leffler Decay of Fourier Modes
  • Modified Kramers-Moyall Expansion for a General Discrete Markov Process
  • Moments of First Passage Time
  • Moments, Cumulants, Scaling
  • Montroll-Weiss Formulation of CTRW
  • Multi dimensional CLT for Sums of IID Random Vectors
  • Non separable Continuous time Random Walks
  • Nonlinear Waves in Traffic Flow, Characteristics, Shocks, Burgers' Equation
  • Non-separable Continuous-time Random Walks
  • Normal vs Anomalous Diffusion
  • Overview of Mechanisms for Anomalous Diffusion
  • Parabola Continuous Laplacian Growth
  • Parabolic Cylinder Functions and Dawson's Integral
  • Percentile Order Statistics, Asymptotics of the Median Versus the Mean
  • Persistent Random Walk to Model Bond-bending Energetic Effects
  • Phase Diagram for Anomalous Diffusion
  • Polubarinova Galin Equation
  • Polya's Theorem
  • Polya's Theorem
  • Polymer Models: Persistence and Self-avoidance
  • Polymer Surface Adsorption
  • Potential Theory using Complex Analysis
  • Power law Tails
  • Probability Generating Functions on the Integers
  • Random Walk to Model Entropic Effects in Polymers
  • Random Walk with Exponentially Decaying Correlations
  • Rechargeable Batteries
  • Reflection Principle Path Counting for Lattice Random Walks, Derivation of the Discrete Arcsine
  • Renewal Theory
  • Restoring Force for Stretching
  • Return Probability on a Lattice
  • Run Tumble Motion
  • Saffman Taylor Fingers
  • Self-avoiding Walk to Model Steric Effects
  • Smirnov Density
  • Solution to the Telegrapher's Equation
  • Square-root Scaling of Normal Diffusion
  • Superdiffusion Limiting Levy Distributions for Steps Infinite Variance
  • Surface Growth, Kardar Parisi Zhang Equation
  • The Arcsine Distribution
  • The Central Limit Theorem and the Diffusion Equation
  • The Void Model for Granular Drainage
  • Time-delayed Flux
  • Wave and Diffusion Limits
  • Weakly Non identical Steps
  • Width of the Central Region when Third Fourth Moments Exist
  • Wiener Process