Branching random walk and searching in trees: final report L. Addario-Berry (McGill University),
Bibliographic record
Abstract
A branching random walk is a Galton-Watson tree T to which the individuals have been assigned spatial positions (in R, say), in the following manner. The root r is placed at the origin. Each child c of the root is independently given a random position Pc; the distribution of each such displacement is given by some real random variable X. More generally, when an individual u has a child v, v appears at position Pv = Pu + Xv, where Xv is an independent copy of X. This yields a natural, though idealized, discrete model of how a population may diffuse over time. Branching random walks are a natural and basic object of study in probability, and are far from being fully understood. Furthermore, branching random walks turn out to have strong connections in other parts of mathematics and theoretical computer science. To highlight a particularly notable example, consider the problem of understanding the minimum (most negative) position of any individual in the n’th generation of T, which we denote Mn. An understanding of this random variable ends up being fundamental for analyzing the expected worst-case behavior of a host of data structures of great interest to the theoretical computer science community. The behavior of the expected value EMn also turns out to be intimately connected to the uniqueness of “travelling-wave ” solutions to a reaction-diffusion equation called the Kolmogorov– Petrovskii–Piskounov equation, given by ∂u 1 ∂
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".