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Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
Forecasting stock returns is a challenging problem due to the highly stochastic nature of the market and the vast array of factors and events that can influence trading volume and prices. Nevertheless it has proven to be an attractive…
Sports data analytics is a relevant topic in applied statistics that has been growing in importance in recent years. In basketball, a player or team has a hot hand when their performance during a match is better than expected or they are on…
The presence of momentum in sports, where the outcome of a previous event affects a following event, is a belief often held by fans, and has been the subject of statistical study for many sports. This paper investigates the presence and…
The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
The length of the longest common subsequences (LCSs) is often used as a similarity measurement to compare two (or more) random words. Below we study its statistical behavior in mean and variance using a Monte-Carlo approach from which we…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Continuous-time event sequences, i.e., sequences consisting of continuous time stamps and associated event types ("marks"), are an important type of sequential data with many applications, e.g., in clinical medicine or user behavior…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the…
From 2020 to 2023, Major League Baseball changed rules affecting team composition, player positioning, and game time. Understanding the effects of these rules is crucial for leagues, teams, players, and other relevant parties to assess…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that…
Box score statistics are the baseline measures of performance for National Collegiate Athletic Association (NCAA) basketball. Between the 2011-2012 and 2015-2016 seasons, NCAA teams performed better at home compared to on the road in nearly…
We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in presence of a constant bias c. At each time-step the walker makes a random jump of length \eta drawn from a continuous…
In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record…
League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest…
We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…
We formulate the head-to-head matchups between Major League Baseball pitchers and batters from 1954 to 2008 as a bipartite network of mutually-antagonistic interactions. We consider both the full network and single-season networks, which…