Lectures on probability, information and large scale behaviour
This book stems from lecture notes prepared by the author over decades of teaching. It is divided into two parts. The first part focuses on classical probability, with the aim of helping students develop a solid intuition about random phenomena. It guides them in translating real-world problems into...
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| Formaat: | Online |
| Taal: | Engels |
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2025
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| Online toegang: | https://admin.library.oapen.org/handle/20.500.12657/103990 |
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| _version_ | 1869531403744444416 |
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| author | Marsili, Matteo |
| author_browse | Marsili, Matteo |
| author_facet | Marsili, Matteo |
| author_sort | Marsili, Matteo |
| collection | Directory of Open Access Books |
| description | This book stems from lecture notes prepared by the author over decades of teaching. It is divided into two parts. The first part focuses on classical probability, with the aim of helping students develop a solid intuition about random phenomena. It guides them in translating real-world problems into probabilistic language and equips them with the tools needed to derive quantitative insights. The second part investigates the typical behaviours that emerge in asymptotic regimes -- such as the law of large numbers, limit theorems, and large deviations -- and elucidates their connection to information theory. This latter part offers a unifying perspective, based on principles of information theory and statistical mechanics, for understanding large-scale phenomena like phase transitions that appear across disciplines such as statistical physics, inference, coding theory, and computer science. |
| format | Online |
| id | doab-20.500.12854ir-162599 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1625992025-07-08T05:04:25Z Lectures on probability, information and large scale behaviour Marsili, Matteo Probability; Information theory; Laws of large numbers; Limit theorems; Large deviations; Statistical mechanics; Statistical inference thema EDItEUR::P Mathematics and Science::PH Physics::PHF Materials / States of matter thema EDItEUR::P Mathematics and Science::PH Physics::PHH Thermodynamics and heat thema EDItEUR::P Mathematics and Science::PH Physics::PHS Statistical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling This book stems from lecture notes prepared by the author over decades of teaching. It is divided into two parts. The first part focuses on classical probability, with the aim of helping students develop a solid intuition about random phenomena. It guides them in translating real-world problems into probabilistic language and equips them with the tools needed to derive quantitative insights. The second part investigates the typical behaviours that emerge in asymptotic regimes -- such as the law of large numbers, limit theorems, and large deviations -- and elucidates their connection to information theory. This latter part offers a unifying perspective, based on principles of information theory and statistical mechanics, for understanding large-scale phenomena like phase transitions that appear across disciplines such as statistical physics, inference, coding theory, and computer science. 2025-07-08T05:04:25Z 2025-07-08T05:04:25Z 2025-07-07T10:10:24Z 2025 book https://admin.library.oapen.org/handle/20.500.12657/103990 https://directory.doabooks.org/handle/20.500.12854/162599 eng open access image/jpeg Attribution 4.0 International https://library.oapen.org/bitstream/20.500.12657/103990/1/9788898587063.pdf 10.22323/9788898587063 10.22323/9788898587063 SCOAP3 c2fbf30c-ef0f-473b-8ee4-03e135ae04d0 SCOAP3 for Books 396 open access |
| spellingShingle | Probability; Information theory; Laws of large numbers; Limit theorems; Large deviations; Statistical mechanics; Statistical inference thema EDItEUR::P Mathematics and Science::PH Physics::PHF Materials / States of matter thema EDItEUR::P Mathematics and Science::PH Physics::PHH Thermodynamics and heat thema EDItEUR::P Mathematics and Science::PH Physics::PHS Statistical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling Marsili, Matteo Lectures on probability, information and large scale behaviour |
| title | Lectures on probability, information and large scale behaviour |
| title_full | Lectures on probability, information and large scale behaviour |
| title_fullStr | Lectures on probability, information and large scale behaviour |
| title_full_unstemmed | Lectures on probability, information and large scale behaviour |
| title_short | Lectures on probability, information and large scale behaviour |
| title_sort | lectures on probability information and large scale behaviour |
| topic | Probability; Information theory; Laws of large numbers; Limit theorems; Large deviations; Statistical mechanics; Statistical inference thema EDItEUR::P Mathematics and Science::PH Physics::PHF Materials / States of matter thema EDItEUR::P Mathematics and Science::PH Physics::PHH Thermodynamics and heat thema EDItEUR::P Mathematics and Science::PH Physics::PHS Statistical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling |
| topic_facet | Probability; Information theory; Laws of large numbers; Limit theorems; Large deviations; Statistical mechanics; Statistical inference thema EDItEUR::P Mathematics and Science::PH Physics::PHF Materials / States of matter thema EDItEUR::P Mathematics and Science::PH Physics::PHH Thermodynamics and heat thema EDItEUR::P Mathematics and Science::PH Physics::PHS Statistical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling |
| url | https://admin.library.oapen.org/handle/20.500.12657/103990 |
| work_keys_str_mv | AT marsilimatteo lecturesonprobabilityinformationandlargescalebehaviour |