%0 Journal Article %T Exact time dependence of the cumulants of a tracer position in a dense lattice gas %+ Laboratoire de Physique de l'ENS Lyon (Phys-ENS) %+ Laboratoire de Physique Théorique de la Matière Condensée (LPTMC) %+ PHysicochimie des Electrolytes et Nanosystèmes InterfaciauX (PHENIX) %A Poncet, Alexis %A Grabsch, Aurélien %A Bénichou, Olivier %A Illien, Pierre %< avec comité de lecture %@ 2470-0045 %J Physical Review E %I American Physical Society (APS) %V 105 %N 5 %P 054139 %8 2022-02-21 %D 2022 %R 10.1103/PhysRevE.105.054139 %Z Physics [physics]Journal articles %X We develop a general method to calculate the exact time dependence of the cumulants of the position of a tracer particle in a dense lattice gas of hardcore particles. More precisely, we calculate the cumulant generating function associated with the position of a tagged particle at arbitrary time, and at leading order in the density of vacancies on the lattice. In particular, our approach gives access to the short-time dynamics of the cumulants of the tracer position-a regime in which few results are known. The generality of our approach is demonstrated by showing that it goes beyond the case of a symmetric 1D random walk, and covers the important situations of (i) a biased tracer; (ii) comb-like structures; and (iii) d-dimensional situations. %G English %2 https://hal.science/hal-03842911/document %2 https://hal.science/hal-03842911/file/2202.09278.pdf %L hal-03842911 %U https://hal.science/hal-03842911 %~ ENS-LYON %~ CNRS %~ UNIV-LYON1 %~ LPTMC %~ INC-CNRS %~ PHENIX %~ SORBONNE-UNIVERSITE %~ SORBONNE-UNIV %~ SU-SCIENCES %~ UDL %~ UNIV-LYON %~ SU-TI %~ ALLIANCE-SU %~ TEST2-HALCNRS %~ CHIMIE-SU