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Năng lượng tự do điểm-điểm bị làm mát cho các bước đi ngẫu nhiên trong các tiềm năng ngẫu nhiên
Tóm tắt
Chúng tôi xem xét một quá trình đi ngẫu nhiên trong một tiềm năng ngẫu nhiên trên một lưới vuông có không gian tùy ý. Tiềm năng là một hàm của môi trường ergodic và các bước đi của quá trình. Tiềm năng tuân theo một giả định về bậc tích phân mà độ nghiêm ngặt của nó liên quan đến việc trộn lẫn của môi trường, trường hợp tốt nhất là môi trường i.i.d. Chúng tôi chứng minh rằng năng lượng tự do theo điểm-điểm trong thể tích vô hạn tồn tại và có một công thức biến thiên theo dạng entropy. Chúng tôi thiết lập các tính chất điều hòa của năng lượng tự do theo điểm-điểm và liên kết nó với năng lượng tự do theo điểm-đường trong thể tích vô hạn và sự biến thiên lớn bị làm mát của quá trình. Một hệ quả là một nguyên lý biến thiên lớn bị làm mát cho quá trình đi ngẫu nhiên trong một môi trường ngẫu nhiên ergodic, với một hàm tốc độ liên tục.
Từ khóa
#quá trình đi ngẫu nhiên #tiềm năng ngẫu nhiên #năng lượng tự do #môi trường ergodic #nguyên lý biến thiên lớnTài liệu tham khảo
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