Class information for:
Level 1: KAC RICE FORMULA//RANDOM ALGEBRAIC POLYNOMIALS//RANDOM POLYNOMIALS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
24654 305 18.5 37%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
205 3       MATHEMATICS//JOURNAL OF NUMBER THEORY//ACTA ARITHMETICA 52461
3266 2             MAHLER MEASURE//KAC RICE FORMULA//RANDOM ALGEBRAIC POLYNOMIALS 1935
24654 1                   KAC RICE FORMULA//RANDOM ALGEBRAIC POLYNOMIALS//RANDOM POLYNOMIALS 305

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 KAC RICE FORMULA authKW 2706568 9% 97% 28
2 RANDOM ALGEBRAIC POLYNOMIALS authKW 2506593 9% 96% 26
3 RANDOM POLYNOMIALS authKW 2274208 13% 55% 41
4 NUMBER OF REAL ZEROS authKW 1642799 6% 86% 19
5 RANDOM TRIGONOMETRIC POLYNOMIAL authKW 901033 4% 75% 12
6 NUMBER OF REAL ROOTS authKW 834292 3% 83% 10
7 EXPECTED DENSITY authKW 514878 2% 86% 6
8 REAL ROOTS authKW 467187 5% 33% 14
9 RANDOM HOLOMORPHIC SECTIONS authKW 450517 2% 75% 6
10 EXPECTED NUMBER OF REAL ZEROS authKW 300346 1% 100% 3

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 6367 62% 0% 189
2 Statistics & Probability 1614 18% 0% 55
3 Mathematics, Applied 1234 26% 0% 79
4 Physics, Mathematical 689 14% 0% 42
5 Computer Science, Theory & Methods 10 2% 0% 7
6 Multidisciplinary Sciences 2 1% 0% 2
7 Telecommunications 0 1% 0% 3
8 Education, Scientific Disciplines 0 0% 0% 1
9 Physics, Multidisciplinary 0 2% 0% 6
10 Mathematical & Computational Biology -0 0% 0% 1

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 INFORMAT COMPUTAT TECHNOL 100115 0% 100% 1
2 CIENCIAS EXACTAS LA PLATA 50057 0% 50% 1
3 NANO ENERGY GRP 50057 0% 50% 1
4 PHYS ENGN LOW TEMP 50057 0% 50% 1
5 ALGORITHM ARITHMET 44493 1% 22% 2
6 MATEMAT ESTADIST LITORAL 30801 1% 15% 2
7 CHAIR INFORMAT TRANSMISS 20021 0% 20% 1
8 BGSMATH 16684 0% 17% 1
9 ETISUMR 8051 9100 0% 9% 1
10 UNITE RECH MATH 8339 1% 4% 2

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 ABEL SYMPOSIA 19005 5% 1% 14
2 INTERNATIONAL MATHEMATICS RESEARCH NOTICES 8557 5% 1% 16
3 JOURNAL OF THEORETICAL PROBABILITY 3133 2% 1% 6
4 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 2136 6% 0% 19
5 JOURNAL OF STATISTICAL PHYSICS 2135 4% 0% 13
6 INDIANA UNIVERSITY MATHEMATICS JOURNAL 2051 2% 0% 7
7 THEORY OF PROBABILITY AND ITS APPLICATIONS 1834 2% 0% 6
8 JOURNAL OF GEOMETRIC ANALYSIS 1762 1% 0% 4
9 ISRAEL JOURNAL OF MATHEMATICS 1697 3% 0% 8
10 ANNALS OF PROBABILITY 1518 2% 0% 7

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 KAC RICE FORMULA 2706568 9% 97% 28 Search KAC+RICE+FORMULA Search KAC+RICE+FORMULA
2 RANDOM ALGEBRAIC POLYNOMIALS 2506593 9% 96% 26 Search RANDOM+ALGEBRAIC+POLYNOMIALS Search RANDOM+ALGEBRAIC+POLYNOMIALS
3 RANDOM POLYNOMIALS 2274208 13% 55% 41 Search RANDOM+POLYNOMIALS Search RANDOM+POLYNOMIALS
4 NUMBER OF REAL ZEROS 1642799 6% 86% 19 Search NUMBER+OF+REAL+ZEROS Search NUMBER+OF+REAL+ZEROS
5 RANDOM TRIGONOMETRIC POLYNOMIAL 901033 4% 75% 12 Search RANDOM+TRIGONOMETRIC+POLYNOMIAL Search RANDOM+TRIGONOMETRIC+POLYNOMIAL
6 NUMBER OF REAL ROOTS 834292 3% 83% 10 Search NUMBER+OF+REAL+ROOTS Search NUMBER+OF+REAL+ROOTS
7 EXPECTED DENSITY 514878 2% 86% 6 Search EXPECTED+DENSITY Search EXPECTED+DENSITY
8 REAL ROOTS 467187 5% 33% 14 Search REAL+ROOTS Search REAL+ROOTS
9 RANDOM HOLOMORPHIC SECTIONS 450517 2% 75% 6 Search RANDOM+HOLOMORPHIC+SECTIONS Search RANDOM+HOLOMORPHIC+SECTIONS
10 EXPECTED NUMBER OF REAL ZEROS 300346 1% 100% 3 Search EXPECTED+NUMBER+OF+REAL+ZEROS Search EXPECTED+NUMBER+OF+REAL+ZEROS

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 BLEHER, P , HOMMA, Y , ROEDER, RKW , (2016) TWO-POINT CORRELATION FUNCTIONS AND UNIVERSALITY FOR THE ZEROS OF SYSTEMS OF SO(N+1)-INVARIANT GAUSSIAN RANDOM POLYNOMIALS.INTERNATIONAL MATHEMATICS RESEARCH NOTICES. VOL. . ISSUE 11. P. 3237 -3278 16 100% 0
2 GAYET, D , WELSCHINGER, JY , (2014) WHAT IS THE TOTAL BETTI NUMBER OF A RANDOM REAL HYPERSURFACE?.JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK. VOL. 689. ISSUE . P. 137-168 13 81% 5
3 KABLUCHKO, Z , ZAPOROZHETS, D , (2014) ASYMPTOTIC DISTRIBUTION OF COMPLEX ZEROS OF RANDOM ANALYTIC FUNCTIONS.ANNALS OF PROBABILITY. VOL. 42. ISSUE 4. P. 1374 -1395 13 81% 3
4 SHIFFMAN, B , (2008) CONVERGENCE OF RANDOM ZEROS ON COMPLEX MANIFOLDS.SCIENCE IN CHINA SERIES A-MATHEMATICS. VOL. 51. ISSUE 4. P. 707 -720 14 88% 7
5 HANIN, B , (2015) CORRELATIONS AND PAIRING BETWEEN ZEROS AND CRITICAL POINTS OF GAUSSIAN RANDOM POLYNOMIALS.INTERNATIONAL MATHEMATICS RESEARCH NOTICES. VOL. . ISSUE 2. P. 381 -421 12 86% 1
6 SHIFFMAN, B , ZELDITCH, S , (2010) NUMBER VARIANCE OF RANDOM ZEROS ON COMPLEX MANIFOLDS, II: SMOOTH STATISTICS.PURE AND APPLIED MATHEMATICS QUARTERLY. VOL. 6. ISSUE 4. P. 1145 -1167 16 73% 4
7 GAYET, D , WELSCHINGER, JY , (2016) BETTI NUMBERS OF RANDOM REAL HYPERSURFACES AND DETERMINANTS OF RANDOM SYMMETRIC MATRICES.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. VOL. 18. ISSUE 4. P. 733 -772 16 64% 0
8 BABER, J , (2012) SCALED CORRELATIONS OF CRITICAL POINTS OF RANDOM SECTIONS ON RIEMANN SURFACES.JOURNAL OF STATISTICAL PHYSICS. VOL. 148. ISSUE 2. P. 250-279 11 100% 3
9 GAYET, D , WELSCHINGER, JY , (2015) EXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDS.JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU. VOL. 14. ISSUE 4. P. 673 -702 14 70% 2
10 MACDONALD, B , (2010) DENSITY OF COMPLEX CRITICAL POINTS OF A REAL RANDOM SO(M+1) POLYNOMIAL.JOURNAL OF STATISTICAL PHYSICS. VOL. 141. ISSUE 3. P. 517-531 11 100% 6

Classes with closest relation at Level 1


Rank Class id link
1 9153 KAHLER METRICS//KAHLER EINSTEIN METRIC//BALANCED METRICS
2 14256 QUANTUM ERGODICITY//DCAIN//EIGENFUNCTION ESTIMATES
3 32718 LINEAR POLARIZATION CONSTANTS//POLARIZATION CONSTANT//PRODUCT OF LINEAR FUNCTIONALS
4 28890 FBI BARGMANN TRANSFORM//COMPLEX PERTURBATION//INFINITE CURVATURE
5 29725 RANDOM DIRICHLET SERIES//GENERALIZED TYPE//ORDER R
6 14786 PLURISUBHARMONIC FUNCTION//COMPLEX MONGE AMPERE OPERATOR//PLURICOMPLEX GREEN FUNCTION
7 28669 FINITARY ISOMORPHISM//SHIFT COUPLING//PALM MEASURE
8 18422 EXCURSION SET//PICKANDS CONSTANT//RICE FORMULA
9 16362 ONE SIDED EXIT PROBLEM//UMR C5626//ONE SIDED BARRIER PROBLEM
10 19740 ISOSPECTRALITY//LAPLACE SPECTRUM//ISOSPECTRAL

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