Related papers: Time-dependent balls and bins model with positive …
In this work we discuss two urn models with general weight sequences $(A,B)$ associated to them, $A=(\alpha_n)_{n\in\N}$ and $B=(\beta_m)_{m\in\N}$, generalizing two well known P\'olya-Eggenberger urn models, namely the so-called sampling…
We consider a two-color P\'{o}lya urn in the case when a fixed number $S$ of balls is added at each step. Assume it is a large urn that is, the second eigenvalue $m$ of the replacement matrix satisfies $1/2<m/S\leq1$. After $n$ drawings,…
We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multi-flavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators.…
The emergence and impact of tipping points have garnered significant interest in both the social and natural sciences. Despite widespread recognition of the importance of feedbacks between human and natural systems, it is often assumed that…
The evolutionary mechanisms of cooperative behavior represent a fundamental topic in complex systems and evolutionary dynamics. Real-world collective interactions, particularly in multi-agent systems, are often characterized by…
We study the mathematical properties of probabilistic processes in which the independent actions of $n$ players (`causes') can influence the outcome of each player (`effects'). In such a setting, each pair of outcomes will generally be…
World models aim to improve robotic decision making by predicting the consequences of actions. However, in practice, their predictions often become unreliable once the robot encounters states outside the training distribution, limiting…
Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…
"The chance to win given a certain move" is an easily obtainable quantity from data and often quoted in gaming statistics. It is also the fundamental quantity that reinforcement learning AI bases on. Unfortunately, this conditional…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best…
We analyze the impact of two equal billiard balls in three ideal situations: when the balls freely slide on the plane of the billiard, when they roll without sliding and when one of them freely slides and the other rolls. In all the cases…
Decision-making on networks can be explained by both homophily and social influence. While homophily drives the formation of communities with similar characteristics, social influence occurs both within and between communities. Social…
When learning from positive and unlabelled data, it is a strong assumption that the positive observations are randomly sampled from the distribution of $X$ conditional on $Y = 1$, where X stands for the feature and Y the label. Most…
This work introduces a Bayesian framework that unifies a wide class of opinion dynamics models. In this framework, an individual's opinion on a topic is the expected value of their belief, represented as a random variable with a prior…
In this work, we consider a binary hypothesis testing problem involving a group of human decision-makers. Due to the nature of human behavior, each human decision-maker observes the phenomenon of interest sequentially up to a random length…
Effective load balancing lies at the heart of many applications in operations. Frequently tackled via the balls-into-bins paradigm, seminal results established the power of two choices in load balancing: a limited amount of costly…
We investigate the equilibrium behavior for the decentralized quadratic cheap talk problem in which an encoder and a decoder, viewed as two decision makers, have misaligned objective functions. In prior work, we have shown that the number…
The prospects of Kahneman and Tversky, Mega Million and Powerball lotteries, St. Petersburg paradox, premature profits and growing losses criticized by Livermore are reviewed under an angle of view comparing mathematical expectations with…
Consider a community where initially, each individual is positive or negative regarding a reform proposal. In each round, individuals gather randomly in fixed rooms of different sizes, and all individuals in a room agree on the majority…