Abstract
The Thematic Project proposed here brings together a significant portion of theProbability and Stochastic Processes research group in the state of São Paulo. This group iswell-established in the Departments of Statistics and Mathematics at USP, Unicamp, UFSCar,and UFABC and has gained international visibility and recognition due to several factors: (i) itsconsistent and noteworthy publications in high-impact journals, (ii) the organization of eventsthat attract leading researchers in the field, (iii) its proven ability to attract and educate bothBrazilian and foreign students in the associated graduate programs, (iv) its role as a hub foryoung Ph.D. graduates in postdoctoral programs, and (v) its robust and long-standing exchangewith researchers from the world's top research centers.This proposal is a continuation of the successful Thematic Projects titled "Stochastic Modelingof Interacting Systems," funded by FAPESP under grant numbers 04/07276-2, 09/52379-8, and2017/10555-0, with the research team now expanded to include additional members. Theexperience gained from previous projects, along with the incorporation and renewal of researchersin this project, enables the team to focus its research activities in the upcoming period on centraland contemporary topics in Probability Theory and Stochastic Processes, as well as related areas.These topics encompass the study of properties of random walks on graphs and interlacements,interacting particle systems, percolation and its variations such as epidemic and rumor models,biological models including mutation-selection and population dynamics, processes in randomenvironments, scaling limits, and aging dynamics of disordered systems. (AU)
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