A stochastic growth process in which particles performing random walks stick irreversibly upon first contact with a cluster, producing branched, fractal-like aggregates whose morphology is dominated by the transport (diffusion) step.

Principle

Competition between random transport and irreversible attachment: when attachment probability on contact is high relative to transport, growth is controlled by diffusion paths, leading to sparse, ramified structures.

Demonstration

Starting from a seed on a lattice, repeatedly launch independent walkers from a distant boundary; when a walker first hits the cluster it becomes part of it, and the resulting cluster shows branching arms and a non-integer fractal dimension.

Misapplication

Modeling a system with substantial detachment, surface diffusion, or reaction-limited sticking as diffusion-limited aggregation yields qualitatively wrong compactness and scaling properties.

Consequence

Generates scale-dependent rough morphologies and screening effects where protruding tips collect most incoming flux; used to model electrodeposition, dielectric breakdown patterns, and some biological growth under diffusion control.

Reversal

Reaction-limited aggregation (low sticking probability) inverts the mechanism: particles collide many times before sticking, producing denser, more compact clusters rather than strongly branched fractals.

Boundary

Applies to irreversible capture dominated by diffusive transport; excludes ballistic deposition, strong advective transport, or mechanisms with significant surface rearrangement or equilibrium reorganization.

Semantic Tension

Often contrasted with reaction-limited aggregation and models that include relaxation or coalescence; the distinguishing feature is that transport, not attachment kinetics, sets the cluster geometry.

Synthesis

Diffusion-limited aggregation is a transport-controlled stochastic clustering process where random-walk arrival and immediate sticking produce branching, fractal aggregates characterized by screening and nontrivial scaling.