DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

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These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Laplace noise distribution

Definition

Assume Countable Choice. For $b > 0$ , let $μ_{b}$ be the probability measure on $R$ concentrated on $(0, + \infty)$ with Lebesgue density $x \mapsto b^{- 1} e^{- x / b}$ there and zero elsewhere. For every Borel set $A \subseteq R$ , define

Lap (b) (A) = \frac{1}{2} μ_{b} (A \cap (0, + \infty)) + \frac{1}{2} μ_{b} ({x > 0 : - x \in A}) .

Thus $Lap (b)$ is the equal mixture of the positive exponential law and its reflection in the origin. Define $Lap (0)$ to be the point mass at $0$ .

Definition references

The exponential probability law with its density

Reflection is Borel measurable

Dwork and Roth, The Algorithmic Foundations of Differential Privacy, Definition 3.2, printed p. 34.

Vadhan, The Complexity of Differential Privacy, §1.5, PDF pp. 7–8.

Depends on

Used by

Laplace mechanism Algorithm
Laplace noise has its stated Lebesgue density Theorem

Dependency tree · two levels

35 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Cynthia Dwork and Aaron Roth, The Algorithmic Foundations of Differential Privacy (standard reference, not scraped)
Salil Vadhan, The Complexity of Differential Privacy, 2017 manuscript (standard reference, not scraped)