LEADER 02813nam 2200589 450 001 9910483941403321 005 20220423135917.0 010 $a1-280-63516-9 010 $a9786610635160 010 $a3-540-33028-3 024 7 $a10.1007/b134090 035 $a(CKB)1000000000282951 035 $a(SSID)ssj0000105913 035 $a(PQKBManifestationID)11132759 035 $a(PQKBTitleCode)TC0000105913 035 $a(PQKBWorkID)10106005 035 $a(PQKB)10952575 035 $a(DE-He213)978-3-540-33028-8 035 $a(MiAaPQ)EBC4643104 035 $a(MiAaPQ)EBC6694715 035 $a(Au-PeEL)EBL6694715 035 $a(PPN)123132630 035 $a(EXLCZ)991000000000282951 100 $a20220423d2006 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe art of random walks /$fAndrs Telcs 205 $a1st ed. 2006. 210 1$aBerlin ;$aHeidelberg :$cSpringer,$d[2006] 210 4$d??2006 215 $a1 online resource (VII, 200 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1885 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-33027-5 320 $aIncludes bibliographical references and index. 327 $aPotential theory and isoperimetric inequalities -- Basic definitions and preliminaries -- Some elements of potential theory -- Isoperimetric inequalities -- Polynomial volume growth -- Local theory -- Motivation of the local approach -- Einstein relation -- Upper estimates -- Lower estimates -- Two-sided estimates -- Closing remarks -- Parabolic Harnack inequality -- Semi-local theory. 330 $aEinstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein?s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality. . 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1885 606 $aRandom walks (Mathematics) 615 0$aRandom walks (Mathematics) 676 $a519.282 700 $aTelcs$b Andrs$01221982 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483941403321 996 $aThe art of random walks$92833875 997 $aUNINA