Linked from

The 26 pages that link to Random walk, each with the reason it gives.

• DiffusionRelated: Many independent random steps produce the large-scale spreading seen in diffusion.

• Inertial navigation systemRelated: Random sensor noise can accumulate into drifting estimates of velocity, attitude, and position.

• Markov chainBroader topic: A random walk on a discrete state space is a common Markov-chain example.

• RandomnessBroader topic: It shows how local random choices can generate large-scale patterns.

• Mean free pathRelated: Repeated free flights and collisions create random-walk transport through matter.

• Wiener processCompared with: Under suitable scaling, random walks converge to Wiener motion, but retain discrete steps before the limit.

• Concentration gradientRelated: Random walks explain how molecular motion yields diffusion without directed particle paths.

• Molecular diffusionNarrower topic: Molecular trajectories can be modeled as random walks whose ensemble produces diffusion.

• Cauchy distributionNarrower topic: Independent Cauchy steps yield a random walk whose displacement remains Cauchy-distributed.

• George PólyaNarrower topic: Pólya’s recurrence theorem is a landmark result about the long-term behavior of random walks.

• MartingaleBroader topic: A zero-drift random walk is a basic discrete-time martingale.

• Exponential sumCompared with: Random phases suggest square-root cancellation, while arithmetic phases can be structured.

• AutocorrelationBroader topic: Its levels can display strong, persistent sample autocorrelation despite uncorrelated increments.

• Gambler’s ruinNarrower topic: The gambler’s fortune is modeled as a walk whose steps represent wins and losses.

• Polymer physicsRelated: An ideal polymer chain can be modeled as a random walk through space.

• Degree matrixRelated: Dividing adjacency entries by vertex degrees produces transition probabilities on an undirected graph.

• Lévy's continuity theoremRelated: Limit theorems for normalized random walks often reduce to convergence of increment characteristic functions.

• Snakes and LaddersRelated: Repeated dice rolls produce an unpredictable route through the board’s fixed transitions.

• Laplacian matrixRelated: Normalized Laplacians are algebraically linked to random walks on graphs.

• Wald's equationRelated: The position at a stopping time is a random sum of the walk's increments.

• Bertrand's ballot theoremNarrower topic: The evolving margin between two candidates is a finite random walk with a fixed endpoint.

• Edge of chaosCompared with: Random motion lacks the structured rule-driven dynamics associated with the edge of chaos.

• Kolmogorov's two-series theoremRelated: Series convergence asks whether accumulated independent increments settle to a finite limit.

• Azuma's inequalityBroader topic: A random walk with bounded step changes supplies a basic setting for martingale deviation bounds.

• Bienaymé's identityBroader topic: For independent steps, the position's variance is the sum of step variances.

• Diffusion and random walksBroader topic: It is the basic discrete model whose accumulated steps produce spreading.