37 citations · 180 across the 24 of their papers we have counts for
25 papers
Vocabulary Growth Fundamentals: Bernstein Functions and Hausdorff Sequences
Łukasz Dębowski
We survey the theory of vocabulary growth founded in the setting of stochastic processes. In particular, we model the expected number of types through Bernstein functions and Hausd…
From Letters to Words and Back: Invertible Coding of Stationary Measures
Łukasz Dębowski
Motivated by problems of statistical language modeling, we consider probability measures on infinite sequences over two countable alphabets of a different cardinality, such as lett…
Corrections of Zipf's and Heaps' Laws Derived from Hapax Rate Models
Łukasz Dębowski
The article introduces corrections to Zipf's and Heaps' laws based on systematic models of the proportion of hapaxes, i.e., words that occur once. The derivation rests on two assum…
Repetition and recurrence times: Dual statements and summable mixing rates
Łukasz Dębowski
By an analogy to the duality between the recurrence time and the longest match length, we introduce a quantity dual to the maximal repetition length, which we call the repetition t…
Multiperiodic Processes: Ergodic Sources with a Sublinear Entropy
Łukasz Dębowski
Several explicit stochastic processes are known to satisfy Hilberg's law, a power-law growth of block entropy conjectured for natural language and recently connected to the neural…
There Are Fewer Facts Than Words: Communication With A Growing Complexity
Łukasz Dębowski
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words u…