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Appl. Math."],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>For the Abelian sandpile model on Sierpi\u0144ski graphs, we investigate several statistics such as average height, height probabilities and looping constant. In particular, we calculate the expected average height of a recurrent sandpile on the finite iterations of the Sierpi\u0144ski gasket and we also give an algorithmic approach for calculating the height probabilities of recurrent sandpiles under stationarity by using the connection between recurrent configurations of the Abelian sandpile Markov chain and uniform spanning trees. We also calculate the expected fraction of vertices of height <jats:italic>i<\/jats:italic> for <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$i\\in \\{0,1,2,3\\}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>i<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mo>{<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                    <mml:mo>}<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> of sandpiles under stationarity and relate the bulk average height to the looping constant on the Sierpi\u0144ski gasket.<\/jats:p>","DOI":"10.1007\/s40314-025-03139-5","type":"journal-article","created":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T23:34:12Z","timestamp":1743896052000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Average height for Abelian sandpiles and the looping constant on Sierpi\u0144ski graphs"],"prefix":"10.1007","volume":"44","author":[{"given":"Nico","family":"Heizmann","sequence":"first","affiliation":[]},{"given":"Robin","family":"Kaiser","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9117-3983","authenticated-orcid":false,"given":"Ecaterina","family":"Sava-Huss","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,5]]},"reference":[{"issue":"4","key":"3139_CR1","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1007\/s00039-018-0446-y","volume":"28","author":"O Angel","year":"2018","unstructured":"Angel O, Hutchcroft T, Nachmias A, Ray G (2018) Hyperbolic and parabolic unimodular random maps. 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