Guido Boffetta – författare

This textbook aims to bridge a longstanding gap by presenting a rigorous yet physics-centered approach to probability theory and its applications. Despite its foundational role across nearly all areas of physics, many students exhibit notable technical and conceptual gaps in even the most basic aspects of probability. Surprisingly, these issues can persist even among those specializing in statistical mechanics.According to the authors, these shortcomings are largely a consequence of how probability is taught within the physics curriculum. Typically, core concepts are introduced early in a fragmented way, often within laboratory courses, and receive only cursory treatment in statistical mechanics classes. In contrast, more comprehensive and mathematically rigorous instruction is usually reserved for advanced graduate-level courses, which often lack a strong connection to physical intuition. This book addresses that imbalance by offering a cohesive and accessible framework tailored to the needs of physics students.

This textbook aims to bridge a longstanding gap by presenting a rigorous yet physics-centered approach to probability theory and its applications. Despite its foundational role across nearly all areas of physics, many students exhibit notable technical and conceptual gaps in even the most basic aspects of probability. Surprisingly, these issues can persist even among those specializing in statistical mechanics.According to the authors, these shortcomings are largely a consequence of how probability is taught within the physics curriculum. Typically, core concepts are introduced early in a fragmented way, often within laboratory courses, and receive only cursory treatment in statistical mechanics classes. In contrast, more comprehensive and mathematically rigorous instruction is usually reserved for advanced graduate-level courses, which often lack a strong connection to physical intuition. This book addresses that imbalance by offering a cohesive and accessible framework tailored to the needs of physics students.

Questo testo, che nasce dall'esperienza didattica degli autori, si propone di introdurre gli aspetti fondamentali della teoria della probabilità e dei processi stocastici, guardando con particolare attenzione alle connessioni con la meccanica statistica, il caos, le applicazioni modellistiche ed i metodi numerici. La prima parte è costituita da un'introduzione generale alla probabilità con particolare enfasi sulla probabilità condizionata, le densità marginali e i teoremi limite. Nella seconda parte, prendendo spunto dal moto Browniano, sono presentati i concetti fondamentali dei processi stocastici (catene di Markov, equazione di Fokker- Planck). La terza parte è una selezione di argomenti avanzati che possono essere trattati in corsi della laurea specialistica.