| 000 | 03144cam a2200397 i 4500 | ||
|---|---|---|---|
| 001 | on1420314089 | ||
| 003 | OCoLC | ||
| 005 | 20240517145709.0 | ||
| 008 | 240209t20242024riua b 000 0 eng d | ||
| 020 |
_a1470467917 _q(pbk.) |
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| 020 |
_a9781470467913 _q(pbk.) |
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| 035 | _a(OCoLC)1420314089 | ||
| 040 |
_aYDX _beng _erda _cYDX _dOCLCO _dYSM _dOCLCO _dEAU _dOCLCO _dUNBCA _dOCLCQ |
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| 066 | _c(S | ||
| 082 | 0 | 4 |
_a510 _qOCoLC |
| 090 | _acolm | ||
| 100 | 1 |
_aBates, Erik, _eauthor. |
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| 245 | 1 | 0 |
_aEmpirical measures, geodesic lengths, and a variational formula in first-passage percolation / _cby Erik Bates. |
| 264 | 1 |
_aProvidence, R.I. : _bAmerican Mathematical Society, _c2024. |
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| 264 | 4 | _c©2024 | |
| 300 |
_axi, 92 pages : _billustrations ; _c26 cm |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_aunmediated _bn _2rdamedia |
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| 338 |
_avolume _bnc _2rdacarrier |
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| 490 | 1 |
_aMemoirs of the American Mathematical Society ; _x0065-9266 ; _vv. 1460 |
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| 500 | _a"January 2024, volume 293, number 1460 (fourth of 7 numbers)." | ||
| 504 | _aIncludes bibliographical references (pages 89-92). | ||
| 650 | 0 | _aProbabilities. | |
| 650 | 7 |
_aprobability. _2aat |
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| 697 |
_923736 _aColeções de Monografias. |
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| 830 | 0 |
_aMemoirs of the American Mathematical Society ; _vv. 1460. _x0065-9266 |
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| 880 | 3 |
_6520-00/(S _a"This monograph resolves - in a dense class of cases - several open problems concerning geodesics in i.i.d. first-passage percolation on Zd. Our primary interest is in the empirical measures of edge-weighs observed along geodesics from 0 to nξ, where ξ is a fixed unit vector. For various dense families of edge-weight distributions, we prove that these empirical measures converge weakly to a deterministic limit as n -> ∞, answering a question of Hoffman. These families include arbitrarily small L∞-perturbations of any given distribution, almost every finitely supported distribution, uncountable collections of continuous distributions, and certain discrete distributions whose atoms can have any prescribed sequence of probabilities. Moreover, the constructions are explicit enough to guarantee examples possessing certain features, for instance: both continuous and discrete distributions whose support is all of [0, ∞), and distributions given by a density function that is k-times differentiable. All results also hold for ξ-directed infinite geodesics. In comparison, we show that if Zd is replaced by the infinite d-ary tree, then any distribution for the weights admits a unique limiting empirical measure along geodesics. In both the lattice and tree cases, our methodology is driven by a new variational formula for the time constant, which requires no assumptions on the edge-weight distribution. Incidentally, this variational approach also allows us to obtain new convergence results for geodesic lengths, which have been unimproved in the subcritical regime since the seminal 1965 manuscript of Hammersley and Welsh." -- _cProvided by publisher |
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| 942 |
_2ddc _cBK _n0 |
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| 948 | _hNO HOLDINGS IN P5A - 11 OTHER HOLDINGS | ||
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_c41160 _d41160 |
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