Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Pólya’s theorem on random walks | Statement: [George Pólya, notableIdea, Pólya’s theorem on random walks]

Target entity: Pólya’s theorem on random walks
Context triple: [George Pólya, notableIdea, Pólya’s theorem on random walks]

• A. Random Walk and the Theory of Brownian Motion
  "Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
• B. Sylvester’s theorem on partitions
  Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
• C. Harmonic Analysis and the Theory of Probability
  Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
• D. Kolmogorov zero–one law
  The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
• E. Erdős–Rényi law of large numbers
  The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Pólya’s theorem on random walks
Triple: [George Pólya, notableIdea, Pólya’s theorem on random walks]

Pólya’s theorem on random walks is a fundamental result in probability theory stating that simple random walks on one- and two-dimensional lattices are recurrent (almost surely return to the starting point infinitely often), while in three or more dimensions they are transient.

Target entity: Pólya’s theorem on random walks
Target entity description: Pólya’s theorem on random walks is a fundamental result in probability theory stating that simple random walks on one- and two-dimensional lattices are recurrent (almost surely return to the starting point infinitely often), while in three or more dimensions they are transient.

• A. Random Walk and the Theory of Brownian Motion
  "Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
• B. Sylvester’s theorem on partitions
  Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
• C. Harmonic Analysis and the Theory of Probability
  Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
• D. Kolmogorov zero–one law
  The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
• E. Erdős–Rényi law of large numbers
  The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
• F. None of above. chosen