We investigate a special sequence of random variables $A(N)$ defined by an exponential power series with independent standard complex Gaussians $(X(k))_{k \geq 1}$. Introduced Hughes, Keating, and O'Connell in the study matrix theory, this relates to Gaussian multiplicative chaos (in particular "holomorphic chaos'' per Najnudel, Paquette, Simm) functions. Soundararajan Zaman recently determined...

Learning in a multiagent environment is complicated by the fact that as other agents learn, the environment eeectively changes. Moreover, other agents' actions are often not directly observable , and the actions taken by the learning agent can strongly bias which range of behaviors are encountered. We deene the concept of a conjectural equilibrium, where all agents' expectations are realized, a...

The Ohno relation is a well-known among multiple zeta values. Hirose, Onozuka, Sato, and the author investigated sum related to presented two types of new relations five conjectural formulas. This paper proves one these

Abstract Let $p_{\{3, 3\}}(n)$ denote the number of $3$ -regular partitions in three colours. Da Silva and Sellers [‘Arithmetic properties 3-regular colours’, Bull. Aust. Math. Soc. 104 (3) (2021), 415–423] conjectured four Ramanujan-like congruences modulo $5$ satisfied by . We confirm these conjectural using theory modular forms.